Partial hyperbolicity for symplectic diffeomorphisms

DOI10.1016/j.anihpc.2005.06.002zbMath1130.37356arXivmath/0412072OpenAlexW2166974840MaRDI QIDQ850169

Vanderlei Horita, Ali Tahzibi

Publication date: 15 November 2006

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412072

zbMATH Keywords

partial hyperbolicitydominated splittingstable ergodicitysymplectic diffeomorphismsrobust transitivity

Mathematics Subject Classification ID

Related Items (20)

Hofer growth of \(C^1\)-generic Hamiltonian flows ⋮ A Franks' lemma for convex planar billiards ⋮ Generic Hamiltonian Dynamical Systems: An Overview ⋮ Symplectic diffeomorphisms with inverse shadowing ⋮ Symplectic diffeomorphisms with limit shadowing ⋮ Billiards in generic convex bodies have positive topological entropy ⋮ Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ A link between topological entropy and Lyapunov exponents ⋮ Volume-preserving diffeomorphisms with the \(\mathcal{M}_0\)-shadowing properties ⋮ A new proof of Franks' lemma for geodesic flows ⋮ Realization of tangent perturbations in discrete and continuous time conservative systems ⋮ A remark on the topological stability of symplectomorphisms ⋮ Abundance of elliptic dynamics on conservative three-flows ⋮ On \(C^1\)-robust transitivity of volume-preserving flows ⋮ Hamiltonian elliptic dynamics on symplectic $4$-manifolds ⋮ Continuum-wise expansive symplectic diffeomorphisms ⋮ Measure expansive symplectic diffeomorphisms and Hamiltonian systems ⋮ C¹-generic symplectic diffeomorphisms: partial hyperbolicity and zero centre Lyapunov exponents ⋮ Hyperbolicity in the volume-preserving scenario

Cites Work

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• Contributions to the stability conjecture
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• Partial hyperbolicity and robust transitivity
• An ergodic closing lemma
• Stably ergodic diffeomorphisms which are not partially hyperbolic
• Persistent nonhyperbolic transitive diffeomorphisms
• Homoclinic points in symplectic and volume-preserving diffeomorphisms
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Quasi-Elliptic Periodic Points in Conservative Dynamical Systems
• The generic symplectic C^{1}-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point

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