Metric Entropy of Nonautonomous Dynamical Systems

Christoph Kawan

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, page 26-52, electronic only
  • ISSN: 2353-0626

Abstract

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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.

How to cite

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Christoph Kawan. "Metric Entropy of Nonautonomous Dynamical Systems." Nonautonomous Dynamical Systems 1 (2014): 26-52, electronic only. <http://eudml.org/doc/266895>.

@article{ChristophKawan2014,
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.},
author = {Christoph Kawan},
journal = {Nonautonomous Dynamical Systems},
keywords = {Nonautonomous dynamical systems; topological entropy; metric entropy; variational principle; nonautonomous dynamical system},
language = {eng},
pages = {26-52, electronic only},
title = {Metric Entropy of Nonautonomous Dynamical Systems},
url = {http://eudml.org/doc/266895},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Christoph Kawan
TI - Metric Entropy of Nonautonomous Dynamical Systems
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
SP - 26
EP - 52, electronic only
AB - 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.
LA - eng
KW - Nonautonomous dynamical systems; topological entropy; metric entropy; variational principle; nonautonomous dynamical system
UR - http://eudml.org/doc/266895
ER -

References

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