Subharmonic Branching in Reversible Systems

Abstract

The branching of subharmonic solutions at a symmetric periodic solution of an autonomous reversible system is studied. Here “symmetric” means “invariant under time reversal.” It is shown that generically each such symmetric periodic solution belongs to a one-parameter family of similar periodic solutions. Along such a family solutions having multipliers that are roots of unity can be met generically. It is shown that at such solutions further branching of subharmonic solutions will generically occur.