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

  1. Lanchares Barrasa, Víctor 1
  2. Pascual Lería, Ana Isabel 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Libro:
VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques
  1. Palacios Latasa, Manuel Pedro (coord.)
  2. Trujillo, David (coord.)
  3. Torrens Iñigo, Juan José (coord.)
  4. Madaune-Tort, Monique (coord.)
  5. López de Silanes Busto, María Cruz (coord.)
  6. Sanz Sáiz, Gerardo (coord.)

Editorial: Prensas de la Universidad de Zaragoza ; Universidad de Zaragoza

ISBN: 84-7733-720-9

Año de publicación: 2003

Páginas: 189-198

Congreso: Jornadas Zaragoza-Pau de Matemática Aplicada y Estadística (8. 2003. Jaca)

Tipo: Aportación congreso

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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.

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