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Generic Dynamics of 4-Dimensional C 2 Hamiltonian Systems

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We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C 2-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].

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Authors and Affiliations

  1. Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Mário Bessa

  2. Departamento de Matemática, ISEG, Universidade Técnica de Lisboa, Rua do Quelhas 6, 1200-781, Lisboa, Portugal

    João Lopes Dias

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  1. Mário Bessa
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  2. João Lopes Dias
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Correspondence to João Lopes Dias.

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Communicated by G. Gallavotti

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Bessa, M., Dias, J.L. Generic Dynamics of 4-Dimensional C 2 Hamiltonian Systems. Commun. Math. Phys. 281, 597–619 (2008). https://doi.org/10.1007/s00220-008-0500-y

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  • DOI: https://doi.org/10.1007/s00220-008-0500-y

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