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

Adriana Buicǎ, Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

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. © 2014 Juliusz Schauder Centre for Nonlinear Studies.
Original languageEnglish
Pages (from-to)403-419
JournalTopological Methods in Nonlinear Analysis
Volume43
Issue number2
Publication statusPublished - 1 Jan 2014

Keywords

  • Lyapunov-Schmidt reduction
  • Period manifold
  • Periodic solution
  • Small parameter
  • The second order bifurcation function

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