Mathematical problems for the next century

From MaRDI portal

Publication:1582494

Jump to:navigation, search

DOI10.1007/BF03025291zbMath0947.01011OpenAlexW2044413922WikidataQ29999839 ScholiaQ29999839MaRDI QIDQ1582494

Stephen Smale

Publication date: 11 October 2000

Published in: The Mathematical Intelligencer (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03025291

Mathematics Subject Classification ID

Mathematics in general (00A05) Future perspectives in mathematics (01A67)

Related Items

Finiteness of relative equilibria of the four-body problem, The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems, Convex but not strictly convex central configurations, Studies of the Petrov module for a family of generalized Liénard integrable systems, Finiteness of polygonal relative equilibria for generalised quasi-homogeneous \(n\)-body problems and \(n\)-body problems in spaces of constant curvature, Bifurcations of limit cycles in a \(Z_6\)-equivariant planar vector field of degree 7, Central configurations in the spatial \(n\)-body problem for \(n=5,6\) with equal masses, Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system, Central configurations of the curved \(N\)-body problem, Computation of focus values with applications, A note on classical ground state energies, Market design and the stability of general equilibrium, On the geometry of polynomial dynamical systems, Limit cycles of a Liénard cubic system with quadratic friction function, Counting central configurations at the bifurcation points, An octahedral equal area partition of the sphere and near optimal configurations of points, Area-preserving surface diffeomorphisms, Learning in the machine: random backpropagation and the deep learning channel, Limit cycles of generalized Liénard polynomial differential systems via averaging theory, Chaotic advection in the restricted four-vortex problem on a sphere, On the closing lemma for planar piecewise smooth vector fields, Some enumeration problems on central configurations at the bifurcation points, Bifurcation of small limit cycles in \(Z_{5}\)-equivariant planar vector fields of order 5, Closing lemmas, A note on hidden transient chaos in the Lorenz system, On the number of limit cycles bifurcating from a non-global degenerated center, A verified ODE solver and the Lorenz attractor, Saari's conjecture for the restricted three-body problem, New stacked central configurations for the planar 5-body problem, Quadratic variations of spherical fractional Brownian motions, On the structure of the semigroup of entire étale mappings, The central configurations of four masses \(x, - x, y, - y\), Upper bounds on the number of limit cycles in generalized Liénard equations of odd type, An approach to the Jacobian conjecture in terms of irreducibility and square-freeness, On stacked planar central configurations with five bodies when one body is removed, Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points, On a Dulac function for the Kukles system, A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers, Twisted stacked central configurations for the spatial seven-body problem, Two classes of stacked central configurations for the spatial \(2n+1\)-body problem: nested regular polyhedra plus one, On the hyperbolicity of Lorenz renormalization, Finiteness of relative equilibria in the planar generalized \(N\)-body problem with fixed subconfigurations, Linearized polynomial maps over finite fields, Bifurcations of critical orbits of invariant potentials with applications to bifurcations of central configurations of the \(N\)-body problem, Existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature, Gestalt switches in Poincaré's prize paper: an inspiration for, but not an instance of, chaos, Characteristic set algorithms for equation solving in finite fields, A computer-assisted proof of the existence of traveling wave solutions to the scalar Euler equations with artificial viscosity, Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2, Rigidity of planar central configurations, Limit cycle bifurcations from a non-degenerate center, The 16th Hilbert problem on algebraic limit cycles, Higher order limit cycle bifurcations from non-degenerate centers, Successive bifurcations at infinity for second order O.D.E's., Symmetric planar central configurations of five bodies: Euler plus two, Inverse problem of central configurations and singular curve in the collinear 4-body problem, Finiteness of central configurations of five bodies in the plane, The \(n\)-body problem in spaces of constant curvature. II: Singularities, Some lower bounds for \(H(n)\) in Hilbert's 16th problem, On the Mathieu conjecture for \(S U(2)\), Two results on homogeneous Hessian nilpotent polynomials, Dynamics in the Schwarzschild isosceles three body problem, Central configurations formed by two twisted regular polygons, Lower bounds for the Hilbert number of polynomial systems, Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11, Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2, An estimation for the number of limit cycles in a Liénard-like perturbation of a quadratic nonlinear center, Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator, Uniqueness and non-uniqueness of limit cycles for piecewise linear differential systems with three zones and no symmetry, Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops, Limit cycles in generalized Liénard systems, Linear stability of relative equilibria in the charged three-body problem, Bounding the number of limit cycles for a polynomial Liénard system by using regular chains, A projection method on measures sets, Bifurcations of limit cycles in a \(Z_{4}\)-equivariant planar polynomial vector field of degree 7, On limit cycles surrounding a singular point, Central configurations of four bodies with an axis of symmetry, The optimal upper bound on the number of generalized Euler configurations, The golden ratio and super central configurations of the \(n\)-body problem, Spherical distribution of 5 points with maximal distance sum, Periodic solutions with nonconstant sign in Abel equations of the second kind, An upper estimate for the number of limit cycles of even-degree Liénard equations in the focus case, Inversion problem, Legendre transform and inviscid Burgers equations, Bendixson-Dulac criterion and reduction to global uniqueness in the problem of estimating the number of limit cycles, On the number of limit cycles of a \(Z_{4}\)-equivariant quintic polynomial system, Images of commuting differential operators of order one with constant leading coefficients, Symbolic computation of limit cycles associated with Hilbert's 16th problem, Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop, Center conditions at infinity for Abel differential equations, Well-distributed great circles on \(\mathbb S^2\), A \({C^\infty}\) closing lemma for Hamiltonian diffeomorphisms of closed surfaces, Iterative approximation of limit cycles for a class of Abel equations, Triple and quadruple nested central configurations for the planar \(n\)-body problem, Compact leaves of structurally stable foliations, Computational cost of the Fekete problem. I: The forces method on the 2-sphere, The \(C^1\) generic diffeomorphism has trivial centralizer, New central configurations for the planar 7-body problem, Central configurations of the five-body problem with equal masses, Cubic Liénard equations with quadratic damping. II., Global cross sections and minimal flows, Coulomb and Riesz gases: The known and the unknown, Planar central configurations of six bodies, Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model, Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers, Tensors in computations, Formalizing the Face Lattice of Polyhedra, A reverse Thomson problem on the unit circle, LOCAL AND GLOBAL BIFURCATIONS TO LIMIT CYCLES IN A CLASS OF LIÉNARD EQUATION, DEFORMATIONS AND INVERSION FORMULAS FOR FORMAL AUTOMORPHISMS IN NONCOMMUTATIVE VARIABLES, An optimization problem for finite point interaction families, Systematic scenario selection: stress testing and the nature of uncertainty, Unnamed Item, Injectivity of non-singular planar maps with one convex component, On the limit cycles for a class of generalized Liénard differential systems, Derandomization from Algebraic Hardness, The number of planar central configurations for the 4–body problem is finite when 3 mass positions are fixed, Upper Bound on the Number of Zeros of Abelian Integrals for Hyperbolic Hamiltonian Systems of Degree Seven, Computability and Computational Complexity of the Evolution of Nonlinear Dynamical Systems, A survey on the blow-up method for fast-slow systems, Centralizers of derived-from-Anosov systems on : rigidity versus triviality, An exponential lower bound for Zadeh's pivot rule, Analytic structures and harmonic measure at bifurcation locus, Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere, Periodic solutions to the Navier-Stokes equation for a viscous incompressible fluid and gas in space \({\mathbb{R}}^n \), Critical recurrence in the real quadratic family, On the uniqueness of convex central configurations in the planar 4-body problem, Unnamed Item, Upper bounds for the number of isolated critical points via the Thom-Milnor theorem, On the minimax spherical designs, On necessary and sufficient conditions for the real Jacobian conjecture, A fast and simple modification of Newton's method avoiding saddle points, Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory, Rigid continuation paths II. structured polynomial systems, Dropping bodies, Finiteness of Spatial Central Configurations with Fixed Subconfigurations, Orbit equivalences of \(\mathbb{R}\)-covered Anosov flows and hyperbolic-like actions on the line. With an appendix written jointly with Jonathan Bowden, Extraproximal approach to calculating equilibriums in pure exchange models, A soft Lasso model for the motion of a ball falling in the non-Newtonian fluid, Accessibility and porosity of harmonic measure at bifurcation locus, Limit cycle enumeration in random vector fields, Solving the Navier-Stokes equation for a viscous incompressible fluid in an \(n\)-dimensional bounded region and in the entire space \(\mathbb{R}^n\), Realizability makes a difference: a complexity gap for sink-finding in USOs, Stability of singular limit cycles for Abel equations revisited, Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis, Toward finiteness of central configurations for the planar six-body problem by symbolic computations. I: Determine diagrams and orders, On the central configurations of the n-body problem, STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE, Bifurcation of Limit Cycles in a 12-Degree Hamiltonian System Under Thirteenth-Order Perturbation, Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems, Unnamed Item, Regular polygon central configurations of the N-body problem with general homogeneous potential, Crossing periodic orbits of nonsmooth Liénard systems and applications, Homoclinic Orbits and Solitary Waves within the Nondissipative Lorenz Model and KdV Equation, Some counterexamples to a generalized Saari’s conjecture, Aggregated Negative Feedback in a Generalized Lorenz Model, Andoyer equations for noncollinear planar central configurations, On the 3-dimensional Hopf bifurcation via averaging theory of third order, Visualization of Four Limit Cycles in Near-Integrable Quadratic Polynomial Systems, FOUR LIMIT CYCLES FROM PERTURBING QUADRATIC INTEGRABLE SYSTEMS BY QUADRATIC POLYNOMIALS, GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH COLLINEAR OR INFINITELY MANY SINGULARITIES, Central Configurations, Super Central Configurations, and Beyond in the n-Body Problem, HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS, Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor, On a transfer theorem for the \(\text{P}\neq \text{NP}\) conjecture, Saari's Conjecture for Elliptical Motions and Minimizing Solutions of the N-body Problem, Uniformly generated submodules of permutation modules over fields of characteristic 0., Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets, A formalization of convex polyhedra based on the simplex method, Unnamed Item, Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System, On the uniqueness of the isosceles trapezoidal central configuration in the 4-body problem for power-law potentials, Mathieu–Zhao subspaces of vertex algebras, NUMERICAL-SYMBOLIC METHODS FOR SEARCHING RELATIVE EQUILIBRIA IN THE RESTRICTED PROBLEM OF FOUR BODIES, Towards uniform online spherical tessellations, The Jacobian conjecture: structure of Keller mappings, The Minimum Euclidean-Norm Point in a Convex Polytope: Wolfe's Combinatorial Algorithm is Exponential, A Representativeness Assessment of the Angell–Korshover 63-Station Network Sampling Based on Reanalysis Temperature Data, Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems, BIFURCATIONS OF LIMIT CYCLES IN A Z₃-EQUIVARIANT VECTOR FIELD OF DEGREE 5, Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games, On the Number of Limit Cycles in Generalized Abel Equations, BIFURCATIONS OF LIMIT CYCLES IN A Z₂-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7, A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials, Book Review: Limit cycles of differential equations, Statistical instability for contracting Lorenz flows, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, Bifurcations in a Cubic System with a Degenerate Saddle Point, INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z₂-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5, Existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi-homogeneous n-body problems and the curved n-body problem, Smoothed analysis for the condition number of structured real polynomial systems, Super central configurations of the n-body problem, EXACT BOUND ON THE NUMBER OF LIMIT CYCLES ARISING FROM A PERIODIC ANNULUS BOUNDED BY A SYMMETRIC HETEROCLINIC LOOP, The Zambelli Attractors of Coupled, Nonlinear Macrodynamics and Knot Theory, AN INSIGHT ON THE FRACTAL POWER LAW FLOW: FROM A HAUSDORFF VECTOR CALCULUS PERSPECTIVE, On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique, A Bendixon–Dulac theorem for some piecewise systems, The Lorenz Attractor, a Paradigm for Chaos, On the Generation of Sampling Schemes for Magnetic Resonance Imaging, A scaling-invariant algorithm for linear programming whose running time depends only on the constraint matrix, Number of central configurations and singular surfaces in the mass space in the collinear four-body problem, Support of the logarithmic equilibrium measure on sets of revolution in R3, ABELIAN INTEGRALS FOR THE ONE-PARAMETER BOGDANOV–TAKENS SYSTEM, Centennial History of Hilbert's 16th Problem, Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point, On the 16th Hilbert problem for algebraic limit cycles, Computability and Dynamical Systems, Estimation of Fekete points, From Parity and Payoff Games to Linear Programming, On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation, Interval Linear Algebra and Computational Complexity, Convex four-body central configurations with some equal masses, Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry, Hardness assumptions in the foundations of theoretical computer science, Polynomials root-finding using a SLEFE-based clipping method, Bounding the number of limit cycles for parametric Liénard systems using symbolic computation methods, The local period function for Hamiltonian systems with applications, Area preserving maps and volume preserving maps between a class of polyhedrons and a sphere, Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time?, Spectrally optimized pointset configurations, Formal Weierstrass integrability for a Liénard differential system, An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems, Convex central configurations of the 4-body problem with two pairs of equal adjacent masses, Spherical cap discrepancy of the diamond ensemble, A nonsmooth van der Pol-Duffing oscillator. I: The sum of indices of equilibria is \(-1\), Relaxation oscillations in a slow-fast predator-prey model with weak Allee effect and Holling-IV functional response, Bifurcations of small limit cycles in Liénard systems with cubic restoring terms, Optimal scaling parameters for sparse grid discretizations, On the Classical Lorenz System, The centralizer of $C^r$-generic diffeomorphisms at hyperbolic basic sets is trivial, On the logarithmic energy of points on \(\mathbb{S}^2\), Symmetry of planar four-body convex central configurations, Strictly convex central configurations of the planar five-body problem, Bifurcations and enumeration of central configurations of some planar restricted problems, Low-energy points on the sphere and the real projective plane, Three-dimensional central configurations in ℍ3 and 𝕊3, Remarks on the inverse problem of the collinear central configurations in the \(N\)-body problem, Global bifurcation analysis of generalized Liénard polynomial dynamical system, Limit cycles near a homoclinic loop connecting a tangent saddle in a perturbed quadratic Hamiltonian system, On the centered co-circular central configurations for the n-body problem, NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM, Stochastic embedding of dynamical systems, New equations for central configurations and generic finiteness, Unnamed Item, BIFURCATION OF LIMIT CYCLES IN A FOURTH-ORDER NEAR-HAMILTONIAN SYSTEM, On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry, Limit cycles of the generalized polynomial Liénard differential equations, Reduction to transversality of curves in the construction of a Dulac function, Sufficient conditions for the existence of at least \(n\) or exactly \(n\) limit cycles for the Liénard differential systems, Statistics of stationary points of random finite polynomial potentials, On the limit cycles of a quintic planar vector field, Spline approximations in the problem of estimating the number of limit cycles of autonomous systems on the plane, Complex dynamics in biological systems arising from multiple limit cycle bifurcation, Graphs and the Jacobian conjecture, The number and distributions of limit cycles for a class of quintic near-Hamiltonian systems, New central configurations for the planar 5-body problem, Unnamed Item, Hilbert's 16th problem for classical Liénard equations of even degree, On an estimate of the number of limit cycles in a quadratic system, Optimal logarithmic energy points on the unit sphere, Legendre transform, Hessian conjecture and tree formula, On limit cycles of the Liénard equation with \(Z_2\) symmetry, On some open problems in planar differential systems and Hilbert's 16th problem, BIFURCATION OF LIMIT CYCLES IN Z₁₀-EQUIVARIANT VECTOR FIELDS OF DEGREE 9, Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation, Collinear central configurations in the n-body problem with general homogeneous potential, Compactification and desingularization of spaces of polynomial Liénard equations, Unnamed Item, Analysis on limit cycles of \(Z_{q}\)-equivariant polynomial vector fields with degree 3 or 4, Central configurations and total collisions for quasihomogeneous \(n\)-body problems, Algorithmic foundations of computable general equilibrium theory, Bifurcations of Central Configurations in the Four-Body Problem with Some Equal Masses, An application of the Krasnoselskii theorem to systems of algebraic equations, Complete Semi-Dynamical Systems, Estimating the number of stable configurations for the generalized Thomson problem, Limit cycles of a class of generalized Liénard polynomial equations, Smale 17th Problem: Advances and Open Directions, A new series of conjectures and open questions in optimization and matrix analysis, Structure and Optimisation in Computational Harmonic Analysis: On Key Aspects in Sparse Regularisation, New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture, ON THE MAXIMUM NUMBER OF LIMIT CYCLES OF A CLASS OF GENERALIZED LIÉNARD DIFFERENTIAL SYSTEMS, EXTENSION OF CHICONE'S METHOD FOR PERTURBATION SYSTEMS OF THREE PARAMETERS WITH APPLICATION TO THE LIENARD SYSTEM, BIFURCATIONS OF LIMIT CYCLES FOR A PERTURBED CUBIC SYSTEM WITH DOUBLE FIGURE EIGHT LOOP, Two limit cycles in Liénard piecewise linear differential systems, Hessian nilpotent polynomials and the Jacobian conjecture, On centered co-circular central configurations of the \(n\)-body problem, Perturbation of a period annulus with a unique two-saddle cycle in higher order Hamiltonian, More limit cycles than expected in Liénard equations, Essential perturbations of polynomial vector fields with a period annulus, Extrema of the Andronov-Hopf function of a polynomial Lienard system, A \(\tau \)-conjecture for Newton polygons, On point energies, separation radius and mesh norm for s-extremal configurations on compact sets in \(\mathbb R^n\), Computing geometric Lorenz attractors with arbitrary precision, Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations, On the number of limit cycles of a monodromic polynomial vector field on the plane, Dziobek configurations of the restricted (N + 1)-body problem with equal masses, Perturbation theory of a symmetric center within Liénard equations, Distributing many points on spheres: minimal energy and designs, The number of planar central configurations is finite when $N-1$ mass positions are fixed, REFLECTIONS ON MATHEMATICAL ECONOMICS IN THE ALGORITHMIC MODE, The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations, Natural dynamical reduction of the three-body problem, Stacked Central Configurations with a Homogeneous Potential in \(\mathbb{R}^3\), On Gegenbauer point processes on the unit interval, On the global minimum of the classical potential energy for clusters bound by many-body forces, Symmetric central configurations and the inverse problem, Limit cycles near a centre and a heteroclinic loop in a near-Hamiltonian differential system, The Jacobian problem for one class of nonpolynomial mappings, Convex central configurations for the \(n\)-body problem, The non-positive circuit weight problem in parametric graphs: a solution based on dioid theory, A cubic Kolmogorov system with six limit cycles, Spatial equilateral chain central configurations of the five-body problem with a homogeneous potential, Cameras seeing cameras geometry, Non-existence and uniqueness of limit cycles in a class of generalized Liénard equations, Limit cycles of multi-parameter polynomial dynamical systems, Centralizers of hyperbolic and kinematic-expansive flows, Constrained high-index saddle dynamics for the solution landscape with equality constraints, Rational solutions of Abel differential equations, Exploring circulations yielding no vortex equilibria, A stochastic optimization algorithm for analyzing planar central and balanced configurations in the \(n\)-body problem, Central configurations on the plane with \(N\) heavy and \(k\) light bodies, \(C^r\)-closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle, Physics-informed distribution transformers via molecular dynamics and deep neural networks, On properties of square-free elements in commutative cancellative monoids, The stochastic shortest path problem: a polyhedral combinatorics perspective, A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time, Super central configurations in the collinear 5-body problem, Central configurations in the planar 6-body problem forming two equilateral triangles, Hilbert's sixteenth problem for polynomial Liénard equations, Poincaré-Andronov-Hopf bifurcation and the local Hilbert's 16th problem, Tropical combinatorial Nullstellensatz and sparse polynomials, Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters, On the distribution of runners on a circle, Global existence of real roots and random Newton flow algorithm for nonlinear system of equations, Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere, Equidistribution of jellium energy for Coulomb and Riesz interactions, Cyclicity of periodic annulus and Hopf cyclicity in perturbing a hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop, Equidistributed icosahedral configurations on the sphere, Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles, Use of projective coordinate descent in the Fekete problem, Next-order asymptotic expansion for \(N\)-marginal optimal transport with Coulomb and Riesz costs, Continua of central configurations with a negative mass in the \(n\)-body problem, Generic finiteness for a class of symmetric planar central configurations of the six-body problem and the six-vortex problem, Finiteness of kite relative equilibria in the five-vortex and five-body problems, The Jacobian conjecture and injectivity conditions, Approximation to uniform distribution in \(\mathrm{SO}(3)\), A proof of Euzébio-Pazim-Ponce's conjectures for a degenerate planar piecewise linear differential system with three zones, On the centralizer of vector fields: criteria of triviality and genericity results, Complexity of sparse polynomial solving: homotopy on toric varieties and the condition metric, Upper bounds of limit cycles in Abel differential equations with invariant curves, Simulating Coulomb and log-gases with hybrid Monte Carlo algorithms, Characterization of the existence of non-trivial limit cycles for generalized Abel equations, Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center, Uncomputably large integral points on algebraic plane curves?, Reduction of kinetic equations to Liénard-Levinson-Smith form: counting limit cycles, Limit cycles of a class of Liénard systems with restoring forces of seventh degree, On limit cycles near two centres and a double homoclinic loop in Liénard differential system, Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two, On the independent perturbation parameters and the number of limit cycles of a type of Liénard system, On equilibrium concyclic configurations, Optimal \(N\)-point configurations on the sphere: ``magic numbers and Smale's 7th problem, Limit cycle bifurcations by perturbing a class of planar quintic vector fields, On stacked central configurations with \(n\) bodies when one body is removed, The inverse problem for homothetic polygonal central configurations, Planar \(N\)-body central configurations with a homogeneous potential, Central configurations in planar \(n\)-body problem with equal masses for \(n=5,6,7\), Bifurcations of limit cycles in a \(Z_8\)-equivariant planar vector field of degree 7, On solving univariate sparse polynomials in logarithmic time, Cauchy-type integrals of algebraic functions, Perturbation from a cubic Hamiltonian with three figure eight-loops, Collinear central configurations and singular surfaces in the mass space, Planar symmetric concave central configurations in Newtonian four-body problems, Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields, Computability, noncomputability, and hyperbolic systems, Limit cycles for some families of smooth and non-smooth planar systems, Floer homologies, with applications, Exact bound on the number of zeros of abelian integrals for two hyper-elliptic Hamiltonian systems of degree 4, Automorphisms of generic gradient vector fields with prescribed finite symmetries, Limit cycles of a Liénard system with symmetry allowing for discontinuity, Parameter identification on abelian integrals to achieve Chebyshev property, The \(n\)-vortex problem on a Riemann sphere, The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan, Computing the homology of semialgebraic sets. I: Lax formulas, Discrete and continuous Green energy on compact manifolds, Symmetries of vector fields: the diffeomorphism centralizer, Central configurations of the five-body problem with two isosceles triangles, Fitting tractable convex sets to support function evaluations, Central configurations in the five-body problem: rhombus plus one, Hilbert's `monkey saddle' and other curiosities in the equilibrium problem of three point particles on a circle for repulsive power law forces, A continuum of relative equilibria in the five-body problem, Numerical construction of spherical \(t\)-designs by Barzilai-Borwein method, Intersection multiplicity of a sparse curve and a low-degree curve, Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven, Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four, Localization of real algebraic hypersurfaces with applications to the enumeration of the classes of relative equilibria of a \((5+1)\)-body problem, Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers, Generation of energy-minimizing point sets on spheres and their application in mesh-free interpolation and differentiation, Approximately controllable finite-dimensional bilinear systems are controllable, Some open problems in low dimensional dynamical systems, Applying the symmetry groups to study the \(n\) body problem, Pathology and asymmetry: centralizer rigidity for partially hyperbolic diffeomorphisms, Echo state networks trained by Tikhonov least squares are \(L^2(\mu)\) approximators of ergodic dynamical systems, Equilateral chains and cyclic central configurations of the planar five-body problem, On the relative equilibria of the (rhombus+1)-body problem, Real \(\tau \)-conjecture for sum-of-squares: a unified approach to lower bound and derandomization, Algorithm for studying polynomial maps and reductions modulo prime number, Cyclicity of canard cycles with hyperbolic saddles located away from the critical curve

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1582494&oldid=13869229"