Bifurcations from one-parameter families of symmetric periodic orbits in reversible systems

Abstract

We study bifurcations from one-parameter families of symmetric periodic orbits in reversible systems and give simple criteria for subharmonic symmetric periodic orbits to be born from the one-parameter families. Our result is illustrated for a generalization of the Hénon-Heiles system. In particular, it is shown that there exist infinitely many families of symmetric periodic orbits bifurcating from a family of symmetric periodic orbits under a general condition. Numerical computations for these bifurcations and symmetric periodic orbits are also given.

Bifurcations of symmetric periodic orbits via Floer homology

“…Bifurcations of symmetric periodic orbits have been studied using different techniques, see for example [11,12,14,25,29,30,31]. In [13], Deng and Xia study bifurcations by looking at generating functions of Hamiltonian diffeomorphisms whose critical points correspond to periodic orbits.…”