Stability diagram for 4D linear periodic systems with applications to homographic solutions

Regina Martínez, Anna Samà, Carles Simó

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)

Abstract

We consider a family of 4-dimensional Hamiltonian time-periodic linear systems depending on three parameters, λ1, λ2 and ε such that for ε = 0 the system becomes autonomous. Using normal form techniques we study stability and bifurcations for ε > 0 small enough. We pay special attention to the d'Alembert case. The results are applied to the study of the linear stability of homographic solutions of the planar three-body problem, for some homogeneous potential of degree -α, 0 < α < 2, including the Newtonian case. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)619-651
JournalJournal of Differential Equations
Volume226
DOIs
Publication statusPublished - 15 Jul 2006

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