Time weighted entropies

• Autorzy: Jörg Schmeling
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

topological entropy; symbolic dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 265-278

Daty

wydano

2000

otrzymano

1999-08-02

poprawiono

1999-12-18

Twórcy

autor

Jörg Schmeling

• FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany

Bibliografia

• [1] L. Barreira and J. Schmeling, Sets of 'non-typical' points have full topological entropy and full Hausdorff dimension, Israel J. Math., to appear.
• [2] R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136.
• [3] Ya. Pesin, Dimension Theory in Dynamical Systems: Contemporary Views and Applications, Chicago Lectures in Math., The Univ. of Chicago Press, 1997.
• [4] Ya. Pesin and B. Pitskel', Topological pressure and the variational principle for noncompact sets, Functional Anal. Appl. 18 (1984), no. 4, 307-318.
• [5] C. Rogers, Hausdorff Measures, Cambridge Univ. Press, 1970.
• [6] J. Schmeling, Entropy preservation under Markov coding, DANSE-preprint 6/99.