Generic dynamics of 4-dimensional C2 Hamiltonian systems

Abstract

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.

References in corpus (2)

• Genericity of zero Lyapunov exponents
• Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2,R) cocycles

Cited by in corpus (10)

• $C^1$-Generic Symplectic Diffeomorphisms: Partial Hyperbolicity and Zero Center Lyapunov Exponents
• On the Stability of the Set of Hyperbolic Closed Orbits of a Hamiltonian
• Shades of Hyperbolicity for Hamiltonians
• Realization of tangent perturbations in discrete and continuous time conservative systems
• Generic Hamiltonian Dynamics
• Generic area-preserving reversible diffeomorphisms
• Hamiltonian elliptic dynamics on symplectic 4-manifolds
• On the entropy of conservative flows
• Hyperbolicity and Stability for Hamiltonian flows
• Contributions to the Geometric and Ergodic Theory of Conservative Flows