Relative equilibria and bifurcations in a 2-D Hamiltonian system in resonance 1:p

• Víctor Lanchares Barrasa ^[1] ; Ana Isabel Pascual Lería ^[1]
  1. [1] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 189-198
• Idioma: inglés
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• Resumen

  • In this work, we focus on a Hamiltonian system with two degrees of freedom whose normal form in a neighborhood of the equilibrium solution up to order two, corresponds to a subtraction of two harmonic oscillators in resonance 1:p, with p an odd number. We introduce appropriate coordinates in the reduced phase space in order to study the existence of relative equilibria and bifurcations in terms of the free parameters of the system. We do this for to the simplest case, the resonance 1:3, and then we comment how these results can be extended for a resonance 1:p with p an odd number.