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

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 Henon-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.