Periodic orbits in analytically perturbed Poisson systems

PHYSICA D-NONLINEAR PHENOMENA

卷:276

Article

Garcia, Isaac A.¹  Hernandez-Bermejo, Benito² 

[1] Univ Lleida, Dept Matemat, Lleida 6925001, Spain

[2] Univ Rey Juan Carlos, Dept Fis, Mostoles Madrid 28933, Spain

关键词: Poisson systems;    Casimir invariants;    Hamiltonian systems;    Perturbation theory;    Limit cycles;    Averaging theory;   

DOI  :  10.1016/j.physd.2014.02.008

来源: Elsevier

【 摘 要 】

Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in U subset of R-n to a planar harmonic oscillator defined on the symplectic leaves. As a consequence, the perturbed vector field can be transformed in the domain U to the Lagrange standard form. On the latter, use can be made of averaging theory up to second order to study the existence, number and bifurcation phenomena of periodic orbits. Examples are given ranging from harmonic oscillators with a potential and Duffing oscillators, to a kind of zero-Hopf singularity analytic normal form. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free