Bifurcations in Hamiltonian Systems with a Reflecting Symmetry

• Maikel Bosschaert ^[1] ; Heinz Hanbmann ^[1]
  1. [1] Universiteit Utrecht (Países Bajos)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 12, Nº 1, 2013, págs. 67-87
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • A reflecting symmetry q → −q of a Hamiltonian system does not leave the symplectic structure dq ∧ d p invariant and is therefore usually associated with a reversible Hamiltonian system. However, if q → −q leads to H → −H, then the equations of motion are invariant under the reflection. Such a symmetry imposes strong restrictions on equilibria with q = 0. We study the possible bifurcations triggered by a zero eigenvalue and describe the simplest bifurcation triggered by non-zero eigenvalues on the imaginary axis.