Publication . Bessa, Mário; Rocha, Jorge; Torres, Maria Joana
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.
Publication . Bessa, Mário; Rocha, Jorge; Torres, Maria Joana
We prove that a Hamiltonian star system, defined on a 2d-dimen- sional symplectic manifold M (d 2), is Anosov. As a consequence we obtain the proof of the stability conjecture for Hamiltonians. This generalizes the 4-dimensional results in Bessa et al. (2010) [5].
