Symbolic extensions in intermediate smoothness on surfaces
[Extensions symboliques en régularité intermédiaire sur les surfaces]
Burguet, David
Annales scientifiques de l'École Normale Supérieure, Tome 45 (2012), p. 337-362 / Harvested from Numdam
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Nous montrons que toute dynamique de classe 𝒞 r avec r>1 sur une surface compacte admet une extension symbolique, i.e. une extension topologique qui est un sous-décalage à alphabet fini. Nous donnons plus précisément une borne (optimale) sur l’infimum de l’entropie topologique de toutes les extensions symboliques. Ceci répond positivement à une conjecture de S. Newhouse and T. Downarowicz en dimension deux et améliore un résultat précédent de l’auteur [11].

We prove that 𝒞 r maps with r>1 on a compact surface have symbolic extensions, i.e., topological extensions which are subshifts over a finite alphabet. More precisely we give a sharp upper bound on the so-called symbolic extension entropy, which is the infimum of the topological entropies of all the symbolic extensions. This answers positively a conjecture of S. Newhouse and T. Downarowicz in dimension two and improves a previous result of the author [11].

Publié le : 2012-01-01
DOI : https://doi.org/10.24033/asens.2167
Classification:  37C05,  37C40,  37A35
Mots clés: structure d'entropie, extension symbolique, théorie de Yomdin 
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     author = {Burguet, David},
     title = {Symbolic extensions in intermediate smoothness on surfaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {45},
     year = {2012},
     pages = {337-362},
     doi = {10.24033/asens.2167},
     mrnumber = {2977622},
     zbl = {1282.37015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2012_4_45_2_337_0}
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Burguet, David. Symbolic extensions in intermediate smoothness on surfaces. Annales scientifiques de l'École Normale Supérieure, Tome 45 (2012) pp. 337-362. doi : 10.24033/asens.2167. http://gdmltest.u-ga.fr/item/ASENS_2012_4_45_2_337_0/

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