1. Characterization of hyperbolicity and generalized shadowing lemma.
- Author
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Dragičević, Davor and Slijepčević, Siniša
- Subjects
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GENERALIZATION , *SHADOWING theorem (Mathematics) , *MATHEMATICAL mappings , *LYAPUNOV exponents , *MATHEMATICAL analysis , *ALGEBRA , *DIFFEOMORPHISMS , *DYNAMICS - Abstract
Mather characterized uniform hyperbolicity of a discrete dynamical system as equivalent to invertibility of an operator on the set of all sequences bounded in norm in the tangent bundle of an orbit. We develop a similar characterization of nonuniform hyperbolicity and show that it is equivalent to invertibility of the same operator on a larger, Fréchet space. We apply it to obtain a condition for a diffeomorphism on the boundary of the set of Anosov diffeomorphisms to be nonuniformly hyperbolic. Finally, we generalize the Shadowing lemma in the same context. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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