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Lebesgue orbit equivalence of multidimensional Borel flows: A picturebook of tilings

Published online by Cambridge University Press:  08 March 2016

KONSTANTIN SLUTSKY
KONSTANTIN SLUTSKY*
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 60607-7045, USA email kslutsky@gmail.com
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Abstract

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The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue orbit equivalence, by which we mean an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non-smooth $\mathbb{R}^{d}$-flows are shown to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 6 , September 2017 , pp. 1966 - 1996
Copyright
© Cambridge University Press, 2016 

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