Shades of hyperbolicity for Hamiltonians

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Mario Bessa (Author) Other; Jorge Rocha (Author) FCUP; Maria Joana Torres (Author) Other

Journal

Title: Nonlinearity

Vol. 26

Pages: 2851-2873

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 14 Citations

Scopus - 14 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-006-6RM

DOI: 10.1088/0951-7715/26/10/2851

Abstract (EN): We prove that a Hamiltonian system H is an element of C-2(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 C-2-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 C-2-Hamiltonian is partially hyperbolic. Finally, we prove that stable weakly-shadowable regular energy hypersurfaces are partially hyperbolic.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23