Periodic orbits in analytically perturbed Poisson systems

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• 作者：Isaac A. Garcí ; a^a ; ^{garcia@matematica.udl.cat" class="auth_mail} ; Benito Herná ; ndez-Bermejo^b ; ^{benito.hernandez@urjc.es" class="auth_mail}
• 关键词：Poisson systems ; Casimir invariants ; Hamiltonian systems ; Perturbation theory ; Limit cycles ; Averaging theory
• 刊名：Physica D
• 出版年：15 May, 2014
• 年：2014
• 卷：276
• 期：Complete
• 页码：1-6
• 全文大小：384 K

文摘

Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in to a planar harmonic oscillator defined on the symplectic leaves. As a consequence, the perturbed vector field can be transformed in the domain 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.