Isochronicity into a family of time-reversible cubic vector fields

DOI10.1016/S0096-3003(99)00267-2zbMath1025.37011WikidataQ126782561 ScholiaQ126782561MaRDI QIDQ1854994

Isaac A. García, Javier Chavarriga, Jaume Giné

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

isochronoous centerplanar cubic vector field

Mathematics Subject Classification ID

Related Items (31)

On the number of algebraically independent Poincaré-Liapunov constants ⋮ Isochronicity for a class of reversible systems ⋮ Linearizability conditions for a cubic system ⋮ A class of ninth degree system with four isochronous centers ⋮ Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems ⋮ Isochronicity of a \(\mathbb{Z}_2\)-equivariant quintic system ⋮ Isochronous centers of Lienard type equations and applications ⋮ Algorithmic derivation of isochronicity conditions ⋮ A new method to determine isochronous center conditions for polynomial differential systems. ⋮ Isochronicity conditions for some planar polynomial systems. II. ⋮ Bifurcation of limit cycles and pseudo-isochronicity at infinity in a septic polynomial vector field ⋮ Classification of the centers and isochronicity for a class of quartic polynomial differential systems ⋮ Bifurcation of limit cycles and pseudo-isochronous center at degenerate singular point in a septic system ⋮ Linearizability problem of resonant degenerate singular point for polynomial differential systems ⋮ Complete classification on center of cubic planar systems symmetric with respect to a straight line ⋮ Isochronicity and linearizability of a planar cubic system ⋮ Linearizability and critical period bifurcations of a generalized Riccati system ⋮ Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation ⋮ Bifurcation of limit cycles and pseudo-isochronicity at degenerate singular point in a septic system ⋮ Isochronicity problem of a higher-order singular point for polynomial differential systems ⋮ The period function for quadratic integrable systems with cubic orbits ⋮ Isochronicity at infinity for a class of polynomial differential system ⋮ Complex planar Hamiltonian systems: linearization and dynamics ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ On the period function of reversible quadratic centers with their orbits inside quartics ⋮ Linearizability of planar polynomial Hamiltonian systems ⋮ Limit cycles and isochronous centers in a class of ninth degree system ⋮ Linearizability conditions of time-reversible cubic systems ⋮ THE JACOBI LAST MULTIPLIER AND ISOCHRONICITY OF LIÉNARD TYPE SYSTEMS ⋮ Isochronicity of bi-centers for symmetric quartic differential systems ⋮ The monotonicity of period function for the codimension four quadratic system \(Q_4\).

Cites Work

• Darboux linearization and isochronous centers with a rational first integral
• Reversible systems
• Isochronous centers of a linear center perturbed by fourth degree homogeneous polynomial
• On the integrability of two-dimensional flows
• The classification of reversible cubic systems with center
• Characterizing isochronous centres by Lie brackets
• Quadratic-like cubic systems
• Linearization of isochronous centers
• A class of reversible cubic systems with an isochronous center
• Isochronous centers of cubic reversible systems
• Isochronous Centers in Planar Polynomial Systems
• Bifurcation of Critical Periods for Plane Vector Fields
• regularity properties of the period function near a center of a planar vector field
• Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
• Integrable systems in the plane with center type linear part
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials
• Isochronous centers of cubic systems with degenerate infinity
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