Symbolic dynamics for one dimensional maps with nonuniform expansion

Lima, Yuri

doi:10.1016/j.anihpc.2019.10.001

Lima, Yuri

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 727-755.

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Résumé

Given a piecewise $C^{1 + β}$ map of the interval, possibly with critical points and discontinuities, we construct a symbolic model for invariant probability measures with nonuniform expansion that do not approach the critical points and discontinuities exponentially fast almost surely. More specifically, for each $χ > 0$ we construct a finite-to-one Hölder continuous map from a countable topological Markov shift to the natural extension of the interval map, that codes the lifts of all invariant probability measures as above with Lyapunov exponent greater than χ almost everywhere.

MR Zbl

DOI : 10.1016/j.anihpc.2019.10.001

Classification : 37B10, 37D25, 37E05
Mots-clés : Interval map, Markov partition, Pesin theory, Symbolic dynamics

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Lima, Yuri. Symbolic dynamics for one dimensional maps with nonuniform expansion. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 727-755. doi : 10.1016/j.anihpc.2019.10.001. http://www.numdam.org/articles/10.1016/j.anihpc.2019.10.001/

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