# An entropy for ${\mathbb{Z}}^{2}$ -actions with finite entropy generators

Fundamenta Mathematicae (1998)

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

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topGeller, 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

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

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