Computational hyperbolicity

Marcin Mazur; Jacek Tabor

doi:10.3934/dcds.2011.29.1175

Article Contents

2011, Volume 29, Issue 3: 1175-1189. Doi: 10.3934/dcds.2011.29.1175

This issue Previous Article Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics Next Article On spiral periodic points and saddles for surface diffeomorphisms

Computational hyperbolicity

Marcin Mazur^1, and
Jacek Tabor^2,

1.
Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków
2.
Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, Grota Roweckiego 6, 30-348 Kraków

Received: January 31, 2010

Revised: June 30, 2010

Published: August 2011

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Abstract

Using semihyperbolicity as a basic tool, we provide a general computer assisted method for verifying hyperbolicity of a given set. As a consequence we obtain that the Hénon attractor is hyperbolic for some parameter values.

Keywords:

Mathematics Subject Classification: Primary: 37D05, 37D20, Secondary: 37M99.

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