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On rationally ergodic and rationally weakly mixing rank-one transformations

Published online by Cambridge University Press:  26 February 2014

IRVING DAI ,
XAVIER GARCIA ,
TUDOR PĂDURARIU  and
CESAR E. SILVA
IRVING DAI
Affiliation:
Harvard College, University Hall, Cambridge, MA 02138, USA email ifdai@college.harvard.edu
XAVIER GARCIA
Affiliation:
University of Minnesota, Minneapolis, MN 55455-0213, USA email garci363@umn.edu
TUDOR PĂDURARIU
Affiliation:
University of California, Los Angeles, CA 90095-1555, USA email tudor_pad@yahoo.com
CESAR E. SILVA
Affiliation:
Department of Mathematics, Williams College, Williamstown, MA 01267, USA email csilva@williams.edu
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Abstract

We study the notions of weak rational ergodicity and rational weak mixing as defined by J. Aaronson [Rational ergodicity and a metric invariant for Markov shifts. Israel J. Math. 27(2) (1977), 93–123; Rational weak mixing in infinite measure spaces. Ergod. Th. & Dynam. Sys. 2012, to appear. http://arxiv.org/abs/1105.3541]. We prove that various families of infinite measure-preserving rank-one transformations possess or do not posses these properties, and consider their relation to other notions of mixing in infinite measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 4 , June 2015 , pp. 1141 - 1164
Copyright
© Cambridge University Press, 2014 

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