Periodic solutions for nonlinear differential systems: the second order bifurcation function

Abstract

We are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second order bifurcation function in more general hypotheses than the ones already existing in the literature. We illustrate our main result constructing a second order bifurcation function for the perturbed symmetric Euler top.

The first and second authors are partially supported by the MICINN/FEDER grant number MTM2011-22877 and by a AGAUR (Generalitat de Catalunya) grant number 2009SGR–381. The first author was also partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0094. The third author is partially supported by the MICINN/FEDER grant MTM2008–03437, by AGAUR grant number 2009SGR–410 and ICREA Academia.