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arXiv · 1212.4874

Shades of Hyperbolicity for Hamiltonians

M. Bessa·J. Rocha·M. J. Torres
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Abstract

We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: 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 stably weakly shadowable regular energy hypersurfaces are partially hyperbolic.

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M. Bessa, J. Rocha, M. J. Torres. 2012-12-19. Shades of Hyperbolicity for Hamiltonians. https://doi.org/10.1088/0951-7715%2F26%2F10%2F2851

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