Bifurcations in biparametric quadratic potentials. II

  1. Lanchares, V. 1
  2. 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:
Chaos

ISSN: 1054-1500

Año de publicación: 1995

Volumen: 5

Número: 3

Páginas: 531-535

Tipo: Artículo

SCOPUS: 2-s2.0-0010163440 WoS: WOS:A1995RV66900006 GOOGLE SCHOLAR

Otras publicaciones en: Chaos

Resumen

Quadratic Hamiltonians with the phase space on the ℒ2 sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance- disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. © 1995 American Institute of Physics.