Geodesic
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
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Given a piecewise C1+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.

DOI : 10.1016/j.anihpc.2019.10.001
Classification : 37B10, 37D25, 37E05
Keywords: Interval map, Markov partition, Pesin theory, Symbolic dynamics 
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     author = {Lima, Yuri},
     title = {Symbolic dynamics for one dimensional maps with nonuniform expansion},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {727--755},
     year = {2020},
     publisher = {Elsevier},
     volume = {37},
     number = {3},
     doi = {10.1016/j.anihpc.2019.10.001},
     mrnumber = {4093615},
     zbl = {1455.37012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.10.001/}
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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

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