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Improved mixing rates for infinite measure-preserving systems

Published online by Cambridge University Press:  30 August 2013

DALIA TERHESIU
DALIA TERHESIU*
Affiliation:
Dipartimento di Matematica, Universitá di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy email daliaterhesiu@gmail.com
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Abstract

In this work, we introduce a new technique for operator renewal sequences associated with dynamical systems preserving an infinite measure that improves the results on mixing rates obtained by Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure. Invent. Math. 1 (2012), 61–110]. Also, this technique allows us to offer a very simple proof of the key result of Melbourne and Terhesiu that provides first-order asymptotics of operator renewal sequences associated with dynamical systems with infinite measure. Moreover, combining techniques used in this work with techniques used by Melbourne and Terhesiu, we obtain first-order asymptotics of operator renewal sequences under some relaxed assumption on the first return map.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 2 , April 2015 , pp. 585 - 614
Copyright
© Cambridge University Press, 2013 

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