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

Autor: Pascual Lería, Ana IsabelLanchares Barrasa, Victor

Tipo de documento: Capítulo de libro

Libro: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques :Jaca, Spain, September 15-17, 2003

Año: 2003  Páginas: 189-198

Texto completo open access 

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.