Families of type III<inf>0</inf> ergodic transformations in distinct orbit equivalent classes

Dooley, AH; Hawkins, J; Ralston, D

Families of type III<inf>0</inf> ergodic transformations in distinct orbit equivalent classes

Dooley, AH

Hawkins, J Ralston, D

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Publication Type:: Journal Article
Citation:: Monatshefte fur Mathematik, 2011, 164 (4), pp. 369 - 381
Issue Date:: 2011-12-01

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Field	Value	Language
dc.contributor.author	Dooley, AH https://orcid.org/0000-0002-2656-3042	en_US
dc.contributor.author	Hawkins, J	en_US
dc.contributor.author	Ralston, D	en_US
dc.date.issued	2011-12-01	en_US
dc.identifier.citation	Monatshefte fur Mathematik, 2011, 164 (4), pp. 369 - 381	en_US
dc.identifier.issn	0026-9255	en_US
dc.identifier.uri	http://hdl.handle.net/10453/115348
dc.description.abstract	A new isomorphism invariant of certain measure preserving flows, using sequences of integers, is introduced. Using this invariant, we are able to construct large families of type III0 systems which are not orbit equivalent. In particular we construct an uncountable family of nonsingular ergodic transformations, each having an associated flow that is approximately transitive (and therefore of zero entropy), with the property that the transformations are pairwise not orbit equivalent. © 2011 Springer-Verlag.	en_US
dc.relation.ispartof	Monatshefte fur Mathematik	en_US
dc.relation.isbasedon	10.1007/s00605-010-0258-0	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Families of type III<inf>0</inf> ergodic transformations in distinct orbit equivalent classes	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	164	en_US
utslib.for	0101 Pure 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	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	164	en_US

Abstract:

A new isomorphism invariant of certain measure preserving flows, using sequences of integers, is introduced. Using this invariant, we are able to construct large families of type III0 systems which are not orbit equivalent. In particular we construct an uncountable family of nonsingular ergodic transformations, each having an associated flow that is approximately transitive (and therefore of zero entropy), with the property that the transformations are pairwise not orbit equivalent. © 2011 Springer-Verlag.

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http://hdl.handle.net/10453/115348