Determination of nonlinear stability for low order resonances by a geometric criterion
- Lanchares, V. 1
- Pascual, A.I. 1
- Elipe, A. 2
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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ISSN: 1560-3547
Any de publicació: 2012
Volum: 17
Número: 3-4
Pàgines: 307-317
Tipus: Article
Altres publicacions en: Regular and Chaotic Dynamics
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Resum
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. © 2012 Pleiades Publishing, Ltd.