arXiv subjects

M. J. Torres

Publications and source records attributed to M. J. Torres.

4 recordsLinked to original sources

arXiv2012

Shades of Hyperbolicity for Hamiltonians

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.

math.DS↗

arXiv2012

Hyperbolicity and Stability for Hamiltonian flows

We prove that a Hamiltonian star system, defined on a 2d-dimensional symplectic manifold M, is Anosov. As a consequence we obtain the proof of the stability conjecture for Hamiltonians. This generalizes the 4-dimensional results in [6].

math.DS↗

arXiv2008

A discrete Faa di Bruno's formula

We derive some formulas that rule the behaviour of finite differences under composition of functions with vector values and arguments.

math.HO↗

arXiv2008

Extension of functions with bounded finite differences

We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original function's finite differences.

math.DG↗