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

Adriana Buicǎ; Jaume Giné; Jaume Llibre

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

Adriana Buicǎ, Jaume Giné, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	403-419
Journal	Topological Methods in Nonlinear Analysis
Volume	43
Issue number	2
Publication status	Published - 1 Jan 2014

Keywords

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

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title = "Periodic solutions for nonlinear differential systems: The second order bifurcation function",

abstract = "We are concerned here with the classical problem of Poincar{\'e} 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. {\textcopyright} 2014 Juliusz Schauder Centre for Nonlinear Studies.",

keywords = "Lyapunov-Schmidt reduction, Period manifold, Periodic solution, Small parameter, The second order bifurcation function",

author = "Adriana Buicǎ and Jaume Gin{\'e} and Jaume Llibre",

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T1 - Periodic solutions for nonlinear differential systems: The second order bifurcation function

AU - Buicǎ, Adriana

AU - Giné, Jaume

AU - Llibre, Jaume

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Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Lyapunov-Schmidt reduction

KW - Period manifold

KW - Periodic solution

KW - Small parameter

KW - The second order bifurcation function

M3 - Article

VL - 43

SP - 403

EP - 419

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

SN - 1230-3429

IS - 2

ER -