Bifurcation of subharmonic solutions in time-reversible systems

Abstract

We study bifurcation of 2πq-periodic solutions in one-parameter families of 2π-periodic time-reversible systems. We obtain generically satisfied conditions which imply the bifurcation of 2q branches of such subharmonic solutions. Whenq≧5 the solutions alongq of these branches are unstable, while the solutions along the otherq branches are stable in a weak sense. Special results hold forq=3 andq=4. We also describe a situation in which there is secundary bifurcation and give a brief discussion of what happens under a perturbation which breaks the time-reversibility.