An analogue of the Variational Principle for group and pseudogroup actions
[Un analogue du principe variationnel pour les actions de groupe et pseudogroupe]
Biś, Andrzej
Annales de l'Institut Fourier, Tome 63 (2013), p. 839-863 / Harvested from Numdam
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On généralise au cas des groupes d’homéomorphismes de type fini la notion d’entropie mesure locale introduite par Brin et Katok [7] pour une seule transformation. On applique la théorie des caractéristiques de type dimension d’un système dynamique élaborée par Pesin [25] pour obtenir une relation entre l’entropie topologique d’un pseudogroupe et d’un groupe d’homéomorphismes d’un espace métrique, définie par Ghys, Langevin et Walczak dans [12], et ses entropies mesure locale. On prouve un analogue du principe variationnel pour les actions de groupe et de pseudogroupe qui nous permet d’étudier les dynamiques locales des feuilletages.

We generalize to the case of finitely generated groups of homeomorphisms the notion of a local measure entropy introduced by Brin and Katok [7] for a single map. We apply the theory of dimensional type characteristics of a dynamical system elaborated by Pesin [25] to obtain a relationship between the topological entropy of a pseudogroup and a group of homeomorphisms of a metric space, defined by Ghys, Langevin and Walczak in [12], and its local measure entropies. We prove an analogue of the Variational Principle for group and pseudogroup actions which allows us to study local dynamics of foliations.

Publié le : 2013-01-01
DOI : https://doi.org/10.5802/aif.2778
Classification:  37C85,  28D20,  37B40
Mots clés: principe variationnel, l’entropie topologique, structures Carathéodory, des mesures de Carathéodory et de dimensions de Carathéodory, l’entropie mesure locale, pseudogroups, feuilletages, mesure de Hausdorff, mesure homogene 
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     title = {An analogue of the Variational Principle for group and pseudogroup actions},
     journal = {Annales de l'Institut Fourier},
     volume = {63},
     year = {2013},
     pages = {839-863},
     doi = {10.5802/aif.2778},
     zbl = {1294.37011},
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Biś, Andrzej. An analogue of the Variational Principle for group and pseudogroup actions. Annales de l'Institut Fourier, Tome 63 (2013) pp. 839-863. doi : 10.5802/aif.2778. http://gdmltest.u-ga.fr/item/AIF_2013__63_3_839_0/

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