Bessa, MárioDias, João Lopes2023-05-242023-05-242008Bessa, M., Dias, J.L. Generic Dynamics of 4-Dimensional C 2 Hamiltonian Systems. Commun. Math. Phys. 281, 597–619 (2008)http://hdl.handle.net/10400.2/13821We 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].engjournal article10.1007/s00220-008-0500-y