Symbolic extensions in intermediate smoothness on surfaces

David Burguet

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 2, page 337-362
  • ISSN: 0012-9593

Abstract

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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].

How to cite

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Burguet, David. "Symbolic extensions in intermediate smoothness on surfaces." Annales scientifiques de l'École Normale Supérieure 45.2 (2012): 337-362. <http://eudml.org/doc/272179>.

@article{Burguet2012,
abstract = {We prove that $\mathcal \{C\}^r$ maps with $r&gt;1$ 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].},
author = {Burguet, David},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {entropy structure; symbolic extension; Yomdin’s theory},
language = {eng},
number = {2},
pages = {337-362},
publisher = {Société mathématique de France},
title = {Symbolic extensions in intermediate smoothness on surfaces},
url = {http://eudml.org/doc/272179},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Burguet, David
TI - Symbolic extensions in intermediate smoothness on surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 2
SP - 337
EP - 362
AB - We prove that $\mathcal {C}^r$ maps with $r&gt;1$ 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].
LA - eng
KW - entropy structure; symbolic extension; Yomdin’s theory
UR - http://eudml.org/doc/272179
ER -

References

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