Linearizability of linear systems perturbed by fifth degree homogeneous polynomials

DOI10.1088/1751-8113/40/22/010zbMath1127.34020OpenAlexW1964176023MaRDI QIDQ5291872

Zhaoping Hu, Valery G. Romanovski, Xingwu Chen

Publication date: 19 June 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/40/22/010

zbMATH Keywords

periodic solutionsisochronicitylinearizabilityplanar polynomial systemscentreDarboux linearization

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (30)

Solution of center-focus problem for a class of cubic systems ⋮ On the non-existence of isochronous tangential centers in Filippov vector fields ⋮ Bi-center problem for some classes of \(\mathbb{Z}_2\)-equivariant systems ⋮ Isochronicity of a \(\mathbb{Z}_2\)-equivariant quintic system ⋮ On the formal integrability problem for planar differential systems ⋮ Rigid centres on the center manifold of tridimensional differential systems ⋮ Integrability of complex planar systems with homogeneous nonlinearities ⋮ Integrability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities ⋮ Isochronicity and normal forms of polynomial systems of ODEs ⋮ Complete classification on center of cubic planar systems symmetric with respect to a straight line ⋮ Linearizability of homogeneous quartic polynomial systems with \(1:-2\) resonance ⋮ An approach to solving systems of polynomials via modular arithmetics with applications ⋮ The problem of bicenter and isochronicity for a class of quasi symmetric planar systems ⋮ Centers and isochronous centers for generalized quintic systems ⋮ Linearizability conditions of time-reversible quartic systems having homogeneous nonlinearities ⋮ A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS ⋮ Isochronicity and linearizability of a planar cubic system ⋮ Linearizability and critical period bifurcations of a generalized Riccati system ⋮ Usage of modular techniques for efficient computation of ideal operations ⋮ Linearizability conditions of a time-reversible quartic-like system ⋮ Linearizability conditions for Lotka-Volterra planar complex quartic systems having homogeneous nonlinearities ⋮ Integrability conditions for Lotka-Volterra planar complex quintic systems ⋮ Non-isochronicity of the center in polynomial Hamiltonian systems ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Strong isochronicity of a center of plane dynamical systems with homogeneous nonlinearities of degree 5 ⋮ Linearizability of planar polynomial Hamiltonian systems ⋮ Linearizability conditions of time-reversible cubic systems ⋮ Isochronicity of bi-centers for symmetric quartic differential systems ⋮ Unnamed Item ⋮ Isochronicity and linearizability of planar polynomial Hamiltonian systems

Uses Software

• FGb
• SINGULAR

This page was built for publication: Linearizability of linear systems perturbed by fifth degree homogeneous polynomials