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• W3101445316 abstract "In this paper we deal with an invariant ergodic hyperbolic measure $mu$ for a diffeomorphism $f,$ assuming that $f$ it is either $C^{1+alpha}$ or $f$ is $C^1$ and the Oseledec splitting of $mu$ is dominated. We show that this system $(f,mu)$ satisfies a weaker and non-uniform version of specification, related with notions studied in several recent papers, including cite{STV,Y, PS, T,Var, Oli}. Our main results have several consequences: as corollaries, we are able to improve the results about quantitative Poincar'e recurrence, removing the assumption of the non-uniform specification property in the main Theorem of cite{STV} that establishes an inequality between Lyapunov exponents and local recurrence properties. Another consequence is the fact that any of such measure is the weak limit of averages of Dirac measures at periodic points, as in cite{Sigmund}. Following cite{Y} and cite{PS}, one can show that the topological pressure can be calculated by considering the convenient weighted sums on periodic points, whenever the dynamics is positive expansive and every measure with pressure close to the topological pressure is hyperbolic." @default.
• W3101445316 created "2020-11-23" @default.
• W3101445316 creator A5010487870 @default.
• W3101445316 creator A5084064406 @default.
• W3101445316 date "2013-04-02" @default.
• W3101445316 modified "2023-10-18" @default.
• W3101445316 title "Non-uniform hyperbolicity and non-uniform specification" @default.
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• W3101445316 doi "https://doi.org/10.1090/s0002-9947-2013-05819-9" @default.
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