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- W2952706327 abstract "Let $f:Mto M$ be a $C^{1+epsilon}$-map on a smooth Riemannian manifold $M$ and let $Lambdasubset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f|Lambda$. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by Bowen, Ruelle, and others in the case of hyperbolic diffeomorphisms. We show that the topological pressure $P_{rm top}(varphi)$ can be computed by the values of the potential $varphi$ on the expanding periodic orbits and also that every hyperbolic ergodic invariant measure is well-approximated by expanding periodic orbits. Moreover, we prove that certain equilibrium states are Bowen measures. Finally, we derive a large deviation result for the periodic orbits whose time averages are apart from the space average of a given hyperbolic invariant measure." @default.
- W2952706327 created "2019-06-27" @default.
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- W2952706327 date "2009-01-14" @default.
- W2952706327 modified "2023-09-27" @default.
- W2952706327 title "On the distribution of periodic orbits" @default.
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