Local entropy theory of a random dynamical system

Dooley, AH; Zhang, G

Local entropy theory of a random dynamical system

Dooley, AH

Zhang, G

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Publication Type:: Journal Article
Citation:: Memoirs of the American Mathematical Society, 2015, 223 (1199), pp. 1 - 106
Issue Date:: 2015-01-01

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Field	Value	Language
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.contributor.author	Zhang, G	en_US
dc.date.issued	2015-01-01	en_US
dc.identifier.citation	Memoirs of the American Mathematical Society, 2015, 223 (1199), pp. 1 - 106	en_US
dc.identifier.issn	0065-9266	en_US
dc.identifier.uri	http://hdl.handle.net/10453/101350
dc.description.abstract	© 2014 by the American Mathematical Society. All rights reserved. In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of ℝ or ℕ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, we introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. We also discuss some variants of this variational principle. We introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply our variational principles to obtain a relationship between these of entropy tuples. Finally, we give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.	en_US
dc.relation.ispartof	Memoirs of the American Mathematical Society	en_US
dc.relation.isbasedon	10.1090/memo/1099	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Local entropy theory of a random dynamical system	en_US
dc.type	Journal Article
utslib.citation.volume	1199	en_US
utslib.citation.volume	223	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.issue	1199	en_US
pubs.publication-status	Published	en_US
pubs.volume	223	en_US

Abstract:

© 2014 by the American Mathematical Society. All rights reserved. In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of ℝ or ℕ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, we introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. We also discuss some variants of this variational principle. We introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply our variational principles to obtain a relationship between these of entropy tuples. Finally, we give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

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http://hdl.handle.net/10453/101350