The critical dimension for G-measures

Mansfield, DF; Dooley, AH

The critical dimension for G-measures

Mansfield, DF Dooley, AH

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Publication Type:: Journal Article
Citation:: Ergodic Theory and Dynamical Systems, 2017, 37 (3), pp. 824 - 836
Issue Date:: 2017-05-01

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Field	Value	Language
dc.contributor.author	Mansfield, DF	en_US
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.date.available	2017-01-01	en_US
dc.date.issued	2017-05-01	en_US
dc.identifier.citation	Ergodic Theory and Dynamical Systems, 2017, 37 (3), pp. 824 - 836	en_US
dc.identifier.issn	0143-3857	en_US
dc.identifier.uri	http://hdl.handle.net/10453/127286
dc.description.abstract	© 2015 Cambridge University Press. The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon-Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to G-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann-Krieger type, the critical dimension is an invariant property on the class of ergodic G-measures.	en_US
dc.relation.ispartof	Ergodic Theory and Dynamical Systems	en_US
dc.relation.isbasedon	10.1017/etds.2015.69	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	The critical dimension for G-measures	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	37	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	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	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	37	en_US

Abstract:

© 2015 Cambridge University Press. The critical dimension of an ergodic non-singular dynamical system is the asymptotic growth rate of sums of consecutive Radon-Nikodým derivatives. This has been shown to equal the average coordinate entropy for product odometers when the size of individual factors is bounded. We extend this result to G-measures with an asymptotic bound on the size of individual factors. Furthermore, unlike von Neumann-Krieger type, the critical dimension is an invariant property on the class of ergodic G-measures.

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http://hdl.handle.net/10453/127286