Publicação

Generic dynamics of 4-dimensional C² Hamiltonian systems

Detalhes bibliográficos
Resumo:	We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].
Autores principais:	Bessa, Mário
Outros Autores:	Dias, João Lopes
Assunto:	Hamiltonian Systems Generic Dynamics Probabilistic Perspective
Ano:	2008
País:	Portugal
Tipo de documento:	artigo
Tipo de acesso:	acesso aberto
Instituição associada:	Universidade de Lisboa
Idioma:	inglês
Origem:	Repositório da Universidade de Lisboa

Descrição
Resumo:	We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C2-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].