Bifurcations in biparametric quadratic potentials

  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

Any de publicació: 1995

Volum: 5

Número: 2

Pàgines: 367-373

Tipus: Article

DOI: 10.1063/1.166107 SCOPUS: 2-s2.0-0010141308 WoS: WOS:A1995RE02800003 GOOGLE SCHOLAR

Altres publicacions en: Chaos

Resum

Numerous dynamical systems are represented by quadratic Hamiltonians with the phase space on the ℒ2 sphere. For a class of these Hamiltonians depending on two parameters, we analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by three types of bifurcations, the pitchfork, the teardrop and the oyster bifurcations. We find that the teardrop bifurcation is associated with a non-elementary fixed point whose Poincaré index is zero. © 1995 American Institute of Physics.