Limit cycle enumeration in random vector fields

DOI10.1090/tran/8936zbMath1525.34058arXiv2007.00724OpenAlexW3039722751MaRDI QIDQ6135811

Publication date: 28 August 2023

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00724

Mathematics Subject Classification ID

Random fields (60G60) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
On the number of connected components of random algebraic hypersurfaces
Exponential rarefaction of real curves with many components
Lower bounds for the Hilbert number of polynomial systems
Percolation of random nodal lines
A unified proof of the weakened Hilbert 16th problem for \(n=2\)
Limit cycles of differential equations
On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
On the nonoscillation of elliptic integrals
Bifurcation of planar vector fields and Hilbert's sixteenth problem
The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
Mathematical problems for the next century
Roots of random polynomials with coefficients of polynomial growth
Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group
Hilbert's sixteenth problem for polynomial Liénard equations
HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
Lower estimates for the expected Betti numbers of random real hypersurfaces
An explicit linear estimate for the number of zeros of Abelian integrals
Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
Nonlinear analogue of the May−Wigner instability transition
Quasialgebraic functions
Topologies of Nodal Sets of Random Band‐Limited Functions
EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS
More limit cycles than expected in Liénard equations
Limit cycles of the generalized polynomial Liénard differential equations
Level Sets and Extrema of Random Processes and Fields
On the number of nodal domains of random spherical harmonics
How many zeros of a random polynomial are real?
A JENSEN INEQUALITY FOR A FAMILY OF ANALYTIC FUNCTIONS AND AN ESTIMATE FOR THE AVERAGE NUMBER OF LIMIT CYCLES
Centennial History of Hilbert's 16th Problem
Linear Holomorphic Partial Differential Equations and Classical Potential Theory
HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
Polynomial systems: a lower bound for the Hilbert numbers
Phase Portraits of Planar Vector Fields: Computer Proofs
Topologies of Random Geometric Complexes on Riemannian Manifolds in the Thermodynamic Limit
What is the degree of a smooth hypersurface?
Expected number of real zeroes of random Taylor series
Local Universality of Zeroes of Random Polynomials
Random Fields and Geometry
Statistics on Hilbert's 16th Problem
Certain Hilbert spaces of entire functions
On the average number of real roots of a random algebraic equation
The infinitesimal 16th Hilbert problem in the quadratic case
Small amplitude limit cycles and the distribution of zeros of families of analytic functions
On the number of closed solutions for polynomial ODE's and a special case of Hilbert's 16th problem.

This page was built for publication: Limit cycle enumeration in random vector fields