The generic symplectic C^{1}-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point

DOI10.1017/S0143385702000706zbMath1030.37037OpenAlexW1970759303MaRDI QIDQ4806355

Marie-Claude Arnaud

Publication date: 6 July 2003

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385702000706

zbMATH Keywords

symplectic diffeomorphismsfour-dimensional manifoldsgeneric results

Mathematics Subject Classification ID

Related Items (13)

A Franks' lemma for convex planar billiards ⋮ Generic Hamiltonian Dynamical Systems: An Overview ⋮ Area-Preserving Diffeomorphisms from theC 1Standpoint ⋮ Partial hyperbolicity for symplectic diffeomorphisms ⋮ Closing lemmas ⋮ Local perturbations of conservativeC¹diffeomorphisms ⋮ A new proof of Franks' lemma for geodesic flows ⋮ Realization of tangent perturbations in discrete and continuous time conservative systems ⋮ Abundance of elliptic dynamics on conservative three-flows ⋮ Approximation des ensembles ω-limites des difféomorphismes par des orbites périodiques ⋮ Hamiltonian elliptic dynamics on symplectic $4$-manifolds ⋮ Continuum-wise expansive symplectic diffeomorphisms ⋮ Partial hyperbolicity or dense elliptic periodic points for 𝐶¹-generic symplectic diffeomorphisms

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