[Propriétés génériques pour des systèmes dynamiques de faible régularité]
En 1980, Yano a montré que, sur une variété différentielle compacte, pour les endomorphismes en toutes dimensions et les homéomorphismes en dimension plus grande que un, l'entropie topologique est génériquement infinie. Il avait été auparavant montré que, pour les endomorphismes Lipschitz continus, l'entropie est toujours finie. Dans cette note, nous étudions ce qui se passe entre la régularité
In 1980, Yano showed that on smooth compact manifolds, for endomorphisms in dimension one or above and homeomorphisms in dimensions greater than one, topological entropy is generically infinite. It had earlier been shown that, for Lipschitz endomorphisms on such spaces, topological entropy is always finite. In this article, we investigate what occurs between
Accepté le :
Publié le :
Edson de Faria 1 ; Peter Hazard 1 ; Charles Tresser 2
@article{CRMATH_2017__355_11_1185_0, author = {Edson de Faria and Peter Hazard and Charles Tresser}, title = {Infinite entropy is generic in {H\"older} and {Sobolev} spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {1185--1189}, publisher = {Elsevier}, volume = {355}, number = {11}, year = {2017}, doi = {10.1016/j.crma.2017.10.016}, language = {en}, }
TY - JOUR AU - Edson de Faria AU - Peter Hazard AU - Charles Tresser TI - Infinite entropy is generic in Hölder and Sobolev spaces JO - Comptes Rendus. Mathématique PY - 2017 SP - 1185 EP - 1189 VL - 355 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2017.10.016 LA - en ID - CRMATH_2017__355_11_1185_0 ER -
Edson de Faria; Peter Hazard; Charles Tresser. Infinite entropy is generic in Hölder and Sobolev spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1185-1189. doi : 10.1016/j.crma.2017.10.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.016/
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Cité par 9 documents. Sources : zbMATH
☆ This work was partially supported by “Projeto Temático Dinâmica em Baixas Dimensões”, FAPESP Grant no. 2011/16265-2 and 2016/25053-8, FAPESP Grant no. 2015/17909-7, Projeto PVE CNPq 401020/2014-2 and CAPES Grant CSF-PVE-S - 88887.117899/2016-00.
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