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This article is cited in 1 scientific paper (total in 1 paper)
Determination of Nonlinear Stability for Low Order Resonances by a Geometric Criterion
Víctor Lancharesa, Ana I. Pascuala, Antonio Elipeb a Departamento Matemáticas y Computación, CIME, Universidad de La Rioja, Univ. de La Rioja, 26004 Logroño, Spain
b Grupo de Mecánica Espacial-IUMA and Centro Universitario de la Defensa de Zaragoza, Univ. de Zaragoza, 50009 Zaragoza, Spain
Abstract:
We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under low order resonances. For resonances of order bigger than two there are several results giving stability conditions, in particular one based on the geometry of the phase flow and a set of invariants. In this paper we show that this geometric criterion is still valid for low order resonances, that is, resonances of order two and resonances of order one. This approach provides necessary stability conditions for both the semisimple and non-semisimple cases, with an appropriate choice of invariants.
Keywords:
nonlinear stability, resonances, normal forms.
Received: 02.03.2012 Accepted: 22.06.2012
Citation:
Víctor Lanchares, Ana I. Pascual, Antonio Elipe, “Determination of Nonlinear Stability for Low Order Resonances by a Geometric Criterion”, Regul. Chaotic Dyn., 17:3-4 (2012), 307–317
Linking options:
https://www.mathnet.ru/eng/rcd404 https://www.mathnet.ru/eng/rcd/v17/i3/p307
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