Bifurcation of critical periods for planar Hamiltonian systems of degree \(2n-1\). (English) Zbl 1212.37077

Chen, Xingwu; Li, Yan; Zou, Lan

J. Sichuan Univ., Nat. Sci. Ed. 46, No. 1, 11-14 (2009).

Summary: The orders of weak centers are determined for a family of planar Hamiltonian systems of degree \(2n-1\) where only odd degree nonlinearities are included and the lowest degree is \(2m-1\). Moreover, local bifurcation of critical periods is studied and it is proved that at most \(m-1\) local critical periods can be produced and the maximum number is achievable.

MSC:

37K50	Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
34C23	Bifurcation theory for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

Hamiltonian system; weak center; isochronous center; polynomial; critical period