# Time weighted entropies

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 1, page 265-278
- ISSN: 0010-1354

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topSchmeling, Jörg. "Time weighted entropies." Colloquium Mathematicae 84/85.1 (2000): 265-278. <http://eudml.org/doc/210805>.

@article{Schmeling2000,

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.},

author = {Schmeling, Jörg},

journal = {Colloquium Mathematicae},

keywords = {topological entropy; symbolic dynamics; non-invariant set},

language = {eng},

number = {1},

pages = {265-278},

title = {Time weighted entropies},

url = {http://eudml.org/doc/210805},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Schmeling, Jörg

TI - Time weighted entropies

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 1

SP - 265

EP - 278

AB - 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.

LA - eng

KW - topological entropy; symbolic dynamics; non-invariant set

UR - http://eudml.org/doc/210805

ER -

## References

top- [1] L. Barreira and J. Schmeling, Sets of 'non-typical' points have full topological entropy and full Hausdorff dimension, Israel J. Math., to appear. Zbl0988.37029
- [2] R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 184 (1973), 125-136. Zbl0274.54030
- [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.

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