DOI10.2140/pjm.2007.229.63zbMath1160.34003OpenAlexW2057720700MaRDI QIDQ952898
Jorge Vitório Pereira, Colin Christopher, Jaume Llibre
Publication date: 14 November 2008
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.2007.229.63
Darboux integrability of the simple chaotic flow with a line equilibria differential system ⋮
Liouvillian integrability of polynomial differential systems ⋮
First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines ⋮
Liouvillian integrability versus Darboux polynomials ⋮
Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine ⋮
Liouvillian and Analytic First Integrals for the Brusselator System ⋮
Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity ⋮
Bifurcation Diagrams and Quotient Topological Spaces Under the Action of the Affine Group of a Family of Planar Quadratic Vector Fields ⋮
Multiplicity of limit cycles and analytic \(m\)-solutions for planar differential systems ⋮
On the integrability of the Einstein-Yang-Mills equations ⋮
Local Darboux first integrals of analytic differential systems ⋮
Chaotic Behavior of a Generalized Sprott E Differential System ⋮
Global dynamical aspects of a generalized Chen-Wang differential system ⋮
On the Darboux integrability of the Hindmarsh-Rose burster ⋮
Algebraic invariant curves and first integrals for Riccati polynomial differential systems ⋮
Geometric analysis of quadratic differential systems with invariant ellipses ⋮
Darboux theory of integrability for polynomial vector fields on 𝕊n ⋮
On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n ⋮
Liouvillian integrability of gravitating static isothermal fluid spheres ⋮
On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor ⋮
Dynamics and Darboux integrability of the \(D_2\) polynomial vector fields of degree 2 in \(\mathbb{R}^3\) ⋮
Polynomial vector fields on algebraic surfaces of revolution ⋮
On the Darboux integrability of the logarithmic galactic potentials ⋮
Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\) ⋮
Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮
Liouvillian integrability of the FitzHugh-Nagumo systems ⋮
On foliations of the real projective plane defined by decomposable pencils of cubics ⋮
A new algorithm for finding rational first integrals of polynomial vector fields ⋮
A survey on the inverse integrating factor ⋮
On the number of invariant conics for the polynomial vector fields defined on quadrics ⋮
Darboux integrating factors: inverse problems ⋮
On the Darboux integrability of polynomial differential systems ⋮
Liouvillian and analytic integrability in a modified Philips model ⋮
Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2 ⋮
Characterization of the Kukles polynomial differential systems having an invariant algebraic curve ⋮
Symbolic computations of first integrals for polynomial vector fields ⋮
Global classification of the planar Lotka-Volterra differential systems according to their configurations of invariant straight lines ⋮
Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus ⋮
Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮
Darboux integrability of a nonlinear financial system ⋮
Liouvillian first integrals of quadratic-linear polynomial differential systems ⋮
Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time ⋮
On a simple model for describing convection of the rotating fluid: integrability, bifurcations and global dynamics ⋮
Some new results on Darboux integrable differential systems ⋮
Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity ⋮
Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral ⋮
Local behavior of planar analytic vector fields via integrability ⋮
On Liouvillian integrability of the first-order polynomial ordinary differential equations ⋮
Bifurcation analysis and integrability in the segmented disc dynamo with mechanical friction ⋮
Integrability of a SIS model ⋮
Darboux theory of integrability in the sparse case ⋮
A note on Liouvillian integrability ⋮
Cubic differential systems with invariant straight lines of total multiplicity eight and four distinct infinite singularities ⋮
Liouvillian and analytic integrability of the quadratic vector fields having an invariant ellipse ⋮
Integrability of the Hide-Skeldon-Acheson dynamo ⋮
Darboux integrability and algebraic invariant surfaces for the Rikitake system ⋮
On the remarkable values of the rational first integrals of polynomial vector fields ⋮
Calculation of singular point quantities at infinity for a type of polynomial differential systems ⋮
On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory ⋮
On symbolic integration of algebraic functions ⋮
An efficient method for computing Liouvillian first integrals of planar polynomial vector fields ⋮
Planar quadratic differential systems with invariant straight lines of total multiplicity four ⋮
Algebraic solutions of plane vector fields ⋮
On the integrability of the SIR epidemic model with vital dynamics ⋮
Qualitative study of a model with Rastall gravity ⋮
On invariant line arrangements ⋮
Planar cubic polynomial differential systems with the maximum number of invariant straight lines ⋮
The generalized Liénard polynomial differential systems \(x^\prime = y\), \(y^\prime = - g(x) - f(x) y\) with \(\deg g = \deg f + 1\) are not Liouvillian integrable ⋮
Computation of invariant curves and identifying the type of critical point ⋮
Darboux invariants for planar polynomial differential systems having an invariant conic ⋮
The Michelson system is neither global analytic, nor Darboux integrable ⋮
Nonintegrability of a class of the Bianchi VI\(_0\) and VII\(_0\) models ⋮
Darboux theory of integrability for a class of nonautonomous vector fields ⋮
Integrability of the Nosé-Hoover equation ⋮
Liouvillian first integrals for Liénard polynomial differential systems ⋮
Integrability of a nuclear spin generator ⋮
Polynomial differential systems having a given Darbouxian first integral ⋮
On the Darboux integrability of Blasius and Falkner-Skan equation ⋮
Darboux integrability and reversible quadratic vector fields ⋮
Bounding the number of remarkable values via Jouanolou's theorem ⋮
Polynomial inverse integrating factors for quadratic differential systems ⋮
Complex dynamics in the segmented disc dynamo ⋮
Unnamed Item ⋮
Invariant curves and integrability of planar \(\mathcal C^r\) differential systems ⋮
Darboux integrability of the stretch-twist-fold flow ⋮
Varieties of local integrability of analytic differential systems and their applications ⋮
Unnamed Item ⋮
On the integrability and the zero-Hopf bifurcation of a Chen-Wang differential system ⋮
THE GEOMETRY OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS AND AN INVARIANT STRAIGHT LINE ⋮
Orbitally universal centers ⋮
Interplay of symmetries, null forms, Darboux polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations ⋮
Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity ⋮
On families \(\boldsymbol{QSL}_{\geq 2}\) of quadratic systems with invariant lines of total multiplicity at least 2 ⋮
Integrability and zero-Hopf bifurcation in the Sprott A system ⋮
Remarks on vector fields with simply connected trajectories and their associated derivations ⋮
Cubic systems with invariant straight lines of total multiplicity eight and with three distinct infinite singularities ⋮
LIOUVILLIAN INTEGRABILITY OF A DETERMINISTIC BUSINESS CYCLE MODEL ⋮
First integrals of Darboux type for a family of 3-dimensional Lotka-Volterra systems ⋮
Puiseux integrability of differential equations ⋮
Integrability of the Rucklidge system
This page was built for publication: Multiplicity of invariant algebraic curves in polynomial vector fields