This article is cited in 8 papers

Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances

C. Vidal, F. Dos Santos

Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, Recife-Pe, Brasil

Abstract: The problem of the stability of an equilibrium position of a nonautonomous $2 \pi$-periodic Hamiltonian system with $n$ degrees of freedom ($n \geqslant 2$), in a nonlinear setting, is studied in the presence of a single third and fourth order resonance. We give conditions of instability in the sense of Lyapunov and formal stability of the equilibrium position, depending on the coefficients of the Hamiltonian function.

Keywords: periodic Hamiltonian system, Lyapunov stability, formal stability, resonance, normal form.

MSC: 37C75, 34D20, 34A25

Received: 30.08.2004
Accepted: 07.12.2004

Language: English

DOI: 10.1070/RD2005v010n01ABEH000303

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