On the stability of equilibria in two degrees of freedom Hamiltonian systems under resonances.

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

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Nonlinear Science

ISSN: 0938-8974

Any de publicació: 2005

Volum: 15

Número: 5

Pàgines: 305-319

Tipus: Article

DOI: 10.1007/S00332-004-0674-1 SCOPUS: 2-s2.0-84867925764 WoS: WOS:000232661100002 GOOGLE SCHOLAR

Altres publicacions en: Journal of Nonlinear Science

Repositori institucional: lock_openAccés obert Editor

Resum

We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, the hypothesis may be extended to more general cases. © 2005 Springer Science+Business Media, Inc.