Computing the critical dimensions of Bratteli-Vershik systems with multiple edges

Dooley, AH; Hagihara, R

Computing the critical dimensions of Bratteli-Vershik systems with multiple edges

Dooley, AH

Hagihara, R

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Publication Type:: Journal Article
Citation:: Ergodic Theory and Dynamical Systems, 2012, 32 (1), pp. 103 - 117
Issue Date:: 2012-02-01

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Field	Value	Language
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.contributor.author	Hagihara, R	en_US
dc.date.issued	2012-02-01	en_US
dc.identifier.citation	Ergodic Theory and Dynamical Systems, 2012, 32 (1), pp. 103 - 117	en_US
dc.identifier.issn	0143-3857	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114859
dc.description.abstract	The critical dimension is an invariant that measures the growth rate of the sums of Radon-Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli-Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon-McMillan-Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces. © Cambridge University Press 2011.	en_US
dc.relation.ispartof	Ergodic Theory and Dynamical Systems	en_US
dc.relation.isbasedon	10.1017/S0143385710000969	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Computing the critical dimensions of Bratteli-Vershik systems with multiple edges	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	32	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	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	32	en_US

Abstract:

The critical dimension is an invariant that measures the growth rate of the sums of Radon-Nikodym derivatives for non-singular dynamical systems. We show that for Bratteli-Vershik systems with multiple edges, the critical dimension can be computed by a formula analogous to the Shannon-McMillan-Breiman theorem. This extends earlier results of Dooley and Mortiss on computing the critical dimensions for product and Markov odometers on infinite product spaces. © Cambridge University Press 2011.

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http://hdl.handle.net/10453/114859