Determination of nonlinear stability for low order resonances by a geometric criterion

  1. Lanchares, V. 1
  2. Pascual, A.I. 1
  3. Elipe, A. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Revista:
Regular and Chaotic Dynamics

ISSN: 1560-3547

Año de publicación: 2012

Volumen: 17

Número: 3-4

Páginas: 307-317

Tipo: Artículo

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DOI: 10.1134/S1560354712030070 SCOPUS: 2-s2.0-84865557157 WoS: WOS:000307281200007 GOOGLE SCHOLAR

Otras publicaciones en: Regular and Chaotic Dynamics

Objetivos de desarrollo sostenible

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2012/00015/001

Resumen

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.