A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory

M. Furi and Maria Patrizia Pera

Vol. 160 (1993), No. 2, 219–244

DOI: 10.2140/pjm.1993.160.219

Abstract

We give a continuation principle for forced oscillations of second order differential equations on not necessarily compact differentiable manifolds. A topological sufficient condition for an equilibrium point to be a bifurcation point for periodic orbits is a straightforward consequence of such a continuation principle. Known results on open sets of euclidean spaces as well as a recent continuation principle for forced oscillations on compact manifolds with nonzero Euler-Poincaré characteristic are also included as particular cases.

Mathematical Subject Classification

Primary: 58F22

Secondary: 34C25, 58E07, 70K40

Milestones

Received: 2 December 1991

Revised: 24 March 1992

Published: 1 October 1993