Semi-hyperbolicity and hyperbolicity

Marcin Mazur; Jacek Tabor; Piotr Kościelniak

doi:10.3934/dcds.2008.20.1029

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2008, Volume 20, Issue 4: 1029-1038. Doi: 10.3934/dcds.2008.20.1029

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Semi-hyperbolicity and hyperbolicity

1.
Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków

Received: January 31, 2007

Revised: August 31, 2007

Published: September 2008

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Abstract

We prove that for $\mathcal{C}^1$-diffeomorfisms semi-hyperbolicity of an invariant set implies its hyperbolicity. Moreover, we provide some exact estimations of hyperbolicity constants by semi-hyperbolicity ones, which can be useful in strict numerical computations.

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

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