Bifurcations in biparametric quadratic potentials
- Lanchares, V. 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: 1054-1500
Any de publicació: 1995
Volum: 5
Número: 2
Pàgines: 367-373
Tipus: Article
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.