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October  2008, 20(4): 1029-1038. doi: 10.3934/dcds.2008.20.1029

Semi-hyperbolicity and hyperbolicity

Marcin Mazur 1, , Jacek Tabor 1, and  Piotr Kościelniak 1,

1. 

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

Received  February 2007 Revised  September 2007 Published  January 2008

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.
Keywords: numerical computations., Hyperbolicity, semi-hyperbolicity.
Mathematics Subject Classification: Primary: 37D05, 37D20, Secondary: 37M9.
Citation: Marcin Mazur, Jacek Tabor, Piotr Kościelniak. Semi-hyperbolicity and hyperbolicity. Discrete & Continuous Dynamical Systems, 2008, 20 (4) : 1029-1038. doi: 10.3934/dcds.2008.20.1029
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