Branches of Periodic Orbits in Reversible Systems

In the typical reversible systems which appear in many applications (symmetric) periodic solutions appear in one-parameter families. In this short survey we describe how these branches of periodic orbits originate from equilibria, terminate at homoclinic orbits, and branch from each other in period-doubling bifurcations or higher order subharmonic bifurcations. Adding external parameters allows to study degenerate cases and the transition from degenerate to non-degenerate situations.