Non linear stability in resonant cases: A geometrical approach.

Autor: Elipe Sánchez, Antonio ; LÓPEZ-MORATALLA, T.; LANCHARES BARRASA, VICTOR; RIAGUAS, A.; 

Tipo de documento: Artículo de revista

Revista: Seminario Matemático García de Galdeano. Publicaciones. ISSN: 0085-6029. Año: 2001. Número: 13. Páginas: 1-12.

Texto completo open access 

Resumen: In systems with two degrees of freedom, Arnold's theorem is used for studying nonlinear stability of the origin when the quadratic part of the Hamiltonian is a nondefinite form. In that case, a previous normalization of the higher orders is needed, which reduces the Hamiltonian to homogeneous polynomials in the actions. However, in the case of resonances, it could not be possible to bring the Hamiltonian to the normal form required by Arnold's theorem. In these cases, we determine the stability from analysis of the normalized phase flow. Normalization up to an arbitrary order by Lie-Deprit transformation is carried out using a generalization of the Lissajous variables.