Generic dynamics of 4-dimensional \(C^{2}\) Hamiltonian systems

DOI10.1007/s00220-008-0500-yzbMath1158.37021arXiv0704.3028OpenAlexW2113743924MaRDI QIDQ2517924

Mário Bessa, João Lopes Dias

Publication date: 12 January 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.3028

zbMATH Keywords

Lyapunov exponentsHamiltonian systemsymplectic manifoldfour-dimensional manifold

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Generic properties, structural stability of dynamical systems (37C20)

Related Items (15)

Generic Hamiltonian Dynamical Systems: An Overview ⋮ The flowbox theorem for divergence-free Lipschitz vector fields ⋮ Kinematic N-expansive continuous dynamical systems ⋮ Hyperbolicity or zero Lyapunov exponents for \(C^2\)-Hamiltonians ⋮ On the entropy of conservative flows ⋮ Realization of tangent perturbations in discrete and continuous time conservative systems ⋮ Generic Hamiltonian dynamics ⋮ The Lyapunov exponents of generic skew-product compact semiflows ⋮ On the stability of the set of hyperbolic closed orbits of a Hamiltonian ⋮ Straighten out coordinates for volume-preserving actions ⋮ Hamiltonian elliptic dynamics on symplectic $4$-manifolds ⋮ C¹-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents ⋮ Contributions to the geometric and ergodic theory of conservative flows ⋮ Hamiltonian suspension of perturbed Poincaré sections and an application ⋮ On shadowing and hyperbolicity for geodesic flows on surfaces

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