Generic dynamics of 4-dimensional C 2 hamiltonian systems

Bessa, Mário; Dias, João Lopes

http://hdl.handle.net/10400.2/13821

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Authors

Bessa, Mário

Dias, João Lopes

Abstract(s)

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].