Generic dynamics of 4-dimensional C2 Hamiltonian systems

Details Generic dynamics of 4-dimensional C2 Hamiltonian systems Generic dynamics of 4-dimensional C2 Hamiltonian systems

2007-04-23

arxiv.org/abs/0704.3028v2

Communications in Mathematical Physics, Vol 281, n{\deg} 1, 597-619, 2008

Mathematics

Dynamical Systems

Scientific paper

10.1007/s00220-008-0500-y

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 every regular energy surface is either Anosov or it is in the closure of energy surfaces with zero Lyapunov exponents a.e. This is in the spirit of the Bochi-Mane dichotomy for area-preserving diffeomorphisms on compact surfaces and its continuous-time version for 3-dimensional volume-preserving flows.

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