An entropy for $ℤ^2$ -actions with finite entropy generators

Geller, W.; Pollicott, M.

An entropy for

ℤ^{2}

-actions with finite entropy generators

Geller, W. ; Pollicott, M.

Fundamenta Mathematicae, Tome 158 (1998), p. 209-220 / Harvested from The Polish Digital Mathematics Library

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Résumé

We study a definition of entropy for $ℤ^{+} \times ℤ^{+}$ -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].

Publié le : 1998-01-01

Zbl 0915.58054

EUDML-ID : urn:eudml:doc:212286

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     author = {W. Geller and M. Pollicott},
     title = {An entropy for $$\mathbb{Z}$^2$ -actions with finite entropy generators},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {209-220},
     zbl = {0915.58054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p209bwm}
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Geller, W.; Pollicott, M. An entropy for $ℤ^2$ -actions with finite entropy generators. Fundamenta Mathematicae, Tome 158 (1998) pp. 209-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p209bwm/

Bibliographie

[00000] [1] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1991), 401-414. | Zbl 0212.29201

[00001] [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. | Zbl 0878.54025

[00002] [3] P. Walters, Ergodic Theory, Springer, Berlin, 1982.