Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new met...

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Detalhes bibliográficos
Autor: Bounemoura, Abed
Tipo de documento: artigo
Data de publicação:2009
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:60914
Acesso em linha:https://ddd.uab.cat/record/60914
Access Level:Acceso aberto
Palavra-chave:Hamilton, Sistemes de
Descrição
Resumo:In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.