Metric entropy of nonautonomous dynamical systems
- Abstract We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion of metric entropy. In particular, invariance with respect to appropriately defined isomorphisms, a power rule, and a Rokhlin-type inequality are proved
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| Author: | Christoph KawanGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1196047 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/119604 |
| ISSN: | 2353-0626OPAC |
| Parent Title (English): | Nonautonomous Dynamical Systems |
| Publisher: | De Gruyter Open |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2013/07/10 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/02/28 |
| Tag: | Nonautonomous dynamical systems; metric entropy; topological entropy; variational principle |
| Volume: | 1 |
| Issue: | 1 |
| First Page: | 26 |
| Last Page: | 52 |
| DOI: | https://doi.org/10.2478/msds-2013-0003 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY-NC-ND 3.0: Creative Commons - Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
