Shades of hyperbolicity for hamiltonians

Bessa, Mário; Rocha, Jorge; Torres, Maria Joana

http://hdl.handle.net/10400.2/13876

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Authors

Bessa, Mário

Rocha, Jorge

Torres, Maria Joana

Abstract(s)

We prove that a Hamiltonian system H ∈ C2(M,R) is globally hyperbolic if any of the following statements hold: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification property. Moreover, we prove that, for a C2-generic Hamiltonian H , the union of the partially hyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset of M. As a consequence, any robustly transitive regular energy hypersurface of a C2-Hamiltonian is partially hyperbolic. Finally, we prove that stable weakly-shadowable regular energy hypersurfaces are partially hyperbolic.