An analogue of the Variational Principle for group and pseudogroup actions

Andrzej Biś[1]

  • [1] University of Lodz Department of Mathematics and Computer Science ul. Banacha 22 90-238 Lodz (Poland)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 3, page 839-863
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Biś, Andrzej. "An analogue of the Variational Principle for group and pseudogroup actions." Annales de l’institut Fourier 63.3 (2013): 839-863. <http://eudml.org/doc/275594>.

@article{Biś2013,
abstract = {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.},
affiliation = {University of Lodz Department of Mathematics and Computer Science ul. Banacha 22 90-238 Lodz (Poland)},
author = {Biś, Andrzej},
journal = {Annales de l’institut Fourier},
keywords = {variational principle; topological entropy; Carathéodory structures; Carathéodory measures and dimensions; local measure entropy; pseudogroups; foliations; Hausdorff measure; homogeneous measure},
language = {eng},
number = {3},
pages = {839-863},
publisher = {Association des Annales de l’institut Fourier},
title = {An analogue of the Variational Principle for group and pseudogroup actions},
url = {http://eudml.org/doc/275594},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Biś, Andrzej
TI - An analogue of the Variational Principle for group and pseudogroup actions
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 3
SP - 839
EP - 863
AB - 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.
LA - eng
KW - variational principle; topological entropy; Carathéodory structures; Carathéodory measures and dimensions; local measure entropy; pseudogroups; foliations; Hausdorff measure; homogeneous measure
UR - http://eudml.org/doc/275594
ER -

References

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