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ArticleOriginal scientific text
Title
Time weighted entropies
Authors 1
Affiliations
- FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany
Abstract
For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.
Keywords
topological entropy, symbolic dynamics
Bibliography
- L. Barreira and J. Schmeling, Sets of 'non-typical' points have full topological entropy and full Hausdorff dimension, Israel J. Math., to appear.
- R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136.
- Ya. Pesin, Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago Lectures in Math., The Univ. of Chicago Press, 1997.
- Ya. Pesin and B. Pitskel', Topological pressure and the variational principle for noncompact sets, Functional Anal. Appl. 18 (1984), no. 4, 307-318.
- C. Rogers, Hausdorff Measures, Cambridge Univ. Press, 1970.
- J. Schmeling, Entropy preservation under Markov coding, DANSE-preprint 6/99.
Pages:
265-278
Main language of publication
English
Received
1999-08-02
Accepted
1999-12-18
Published
2000
Exact and natural sciences