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

Adriana Buică, Jaume Giné, Jaume Llibre

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.

Keywords


Periodic solution; Lyapunov-Schmidt reduction; period manifold; small parameter; the second order bifurcation function

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