An entropy for ℤ 2 -actions with finite entropy generators

W. Geller; M. Pollicott

Fundamenta Mathematicae (1998)

  • Volume: 157, Issue: 2-3, page 209-220
  • ISSN: 0016-2736

Abstract

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We study a definition of entropy for ℤ + × ℤ + -actions (or ℤ 2 -actions) due to S. Friedland. Unlike the more traditional definition, this is better suited for actions whose generators have finite entropy as single transformations. We compute its value in several examples. In particular, we settle a conjecture of Friedland [2].

How to cite

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Geller, W., and Pollicott, M.. "An entropy for $ℤ^2$ -actions with finite entropy generators." Fundamenta Mathematicae 157.2-3 (1998): 209-220. <http://eudml.org/doc/212286>.

@article{Geller1998,
abstract = {We study a definition of entropy for $ℤ^+ × ℤ^+$-actions (or $ℤ^2$-actions) due to S. Friedland. Unlike the more traditional definition, this is better suited for actions whose generators have finite entropy as single transformations. We compute its value in several examples. In particular, we settle a conjecture of Friedland [2].},
author = {Geller, W., Pollicott, M.},
journal = {Fundamenta Mathematicae},
keywords = {entropy; -actions; conjecture of Friedland},
language = {eng},
number = {2-3},
pages = {209-220},
title = {An entropy for $ℤ^2$ -actions with finite entropy generators},
url = {http://eudml.org/doc/212286},
volume = {157},
year = {1998},
}

TY - JOUR
AU - Geller, W.
AU - Pollicott, M.
TI - An entropy for $ℤ^2$ -actions with finite entropy generators
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 2-3
SP - 209
EP - 220
AB - We study a definition of entropy for $ℤ^+ × ℤ^+$-actions (or $ℤ^2$-actions) due to S. Friedland. Unlike the more traditional definition, this is better suited for actions whose generators have finite entropy as single transformations. We compute its value in several examples. In particular, we settle a conjecture of Friedland [2].
LA - eng
KW - entropy; -actions; conjecture of Friedland
UR - http://eudml.org/doc/212286
ER -

References

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  1. [1] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1991), 401-414. Zbl0212.29201
  2. [2] S. Friedland, Entropy of graphs, semi-groups and groups, in: Ergodic Theory of ℤ d -actions, M. Pollicott and K. Schmidt (eds.), London Math. Soc. Lecture Note Ser. 228, Cambridge Univ. Press, Cambridge, 1996, 319-343. Zbl0878.54025
  3. [3] P. Walters, Ergodic Theory, Springer, Berlin, 1982. 

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