Metric Entropy of Nonautonomous Dynamical Systems
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, an...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-01-01
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| Series: | Nonautonomous Dynamical Systems |
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| Online Access: | http://www.degruyter.com/view/j/msds.2014.1.issue-1/msds-2013-0003/msds-2013-0003.xml?format=INT |
| _version_ | 1818274400235945984 |
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| author | Kawan Christoph |
| author_facet | Kawan Christoph |
| author_sort | Kawan Christoph |
| collection | DOAJ |
| description | 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 |
| first_indexed | 2024-12-12T22:13:15Z |
| format | Article |
| id | doaj.art-41aa46f1127448f0b8de4e31294b81fb |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-12-12T22:13:15Z |
| publishDate | 2014-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-41aa46f1127448f0b8de4e31294b81fb2022-12-22T00:10:10ZengDe GruyterNonautonomous Dynamical Systems2353-06262014-01-011110.2478/msds-2013-0003msds-2013-0003Metric Entropy of Nonautonomous Dynamical SystemsKawan Christoph0Institut für Mathematik, Universität Augsburg, 86159 Augsburg, GermanyWe 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 provedhttp://www.degruyter.com/view/j/msds.2014.1.issue-1/msds-2013-0003/msds-2013-0003.xml?format=INTNonautonomous dynamical systemstopological entropymetric entropyvariational principle |
| spellingShingle | Kawan Christoph Metric Entropy of Nonautonomous Dynamical Systems Nonautonomous Dynamical Systems Nonautonomous dynamical systems topological entropy metric entropy variational principle |
| title | Metric Entropy of Nonautonomous Dynamical Systems |
| title_full | Metric Entropy of Nonautonomous Dynamical Systems |
| title_fullStr | Metric Entropy of Nonautonomous Dynamical Systems |
| title_full_unstemmed | Metric Entropy of Nonautonomous Dynamical Systems |
| title_short | Metric Entropy of Nonautonomous Dynamical Systems |
| title_sort | metric entropy of nonautonomous dynamical systems |
| topic | Nonautonomous dynamical systems topological entropy metric entropy variational principle |
| url | http://www.degruyter.com/view/j/msds.2014.1.issue-1/msds-2013-0003/msds-2013-0003.xml?format=INT |
| work_keys_str_mv | AT kawanchristoph metricentropyofnonautonomousdynamicalsystems |