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

• Autorzy: W. Geller , M. Pollicott
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 28-++: Measure and integration
• 58-++: Global analysis, analysis on manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 157
• Numer: 2-3
• Strony: 209-220

Daty

wydano

1998

otrzymano

1997-09-11

poprawiono

1998-02-16

Twórcy

autor

W. Geller

• Department of Mathematics, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216, U.S.A.

autor

M. Pollicott

Bibliografia

• [1] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1991), 401-414.
• [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.
• [3] P. Walters, Ergodic Theory, Springer, Berlin, 1982.