engleski

Characterization of hyperbolicity and generalized shadowing lemma

J. 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 di¤eomorphism on the boundary of the set of Anosov di¤eomorphisms to be nonuniformly hyperbolic. Finally we generalise the Shadowing lemma in the same context.

hyperbolicity; Lyapunov exponents; shadowing; Anosov maps

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