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Transactions of the American Mathematical Society

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Rates of mixing for non-Markov infinite measure semiflows


Authors: Henk Bruin, Ian Melbourne and Dalia Terhesiu
Journal: Trans. Amer. Math. Soc. 371 (2019), 7343-7386
MSC (2010): Primary 37A25; Secondary 37A40, 37A50, 37D25
DOI: https://doi.org/10.1090/tran/7582
Published electronically: October 24, 2018
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Abstract: We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincaré map that is uniformly expanding and Markov. As illustrations of the method, we consider semiflows over non-Markov Pomeau-Manneville intermittent maps with infinite measure, and we also obtain mixing rates for semiflows over Collet-Eckmann maps with nonintegrable roof function.


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Additional Information

Henk Bruin
Affiliation: Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria

Ian Melbourne
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Dalia Terhesiu
Affiliation: Mathematics Department, University of Exeter, Exeter EX4 4QF, United Kingdom

DOI: https://doi.org/10.1090/tran/7582
Keywords: Mixing, semiflow, renewal theory, non-Markov, intermittency
Received by editor(s): May 22, 2017
Received by editor(s) in revised form: September 22, 2017, January 31, 2018, and March 20, 2018
Published electronically: October 24, 2018
Additional Notes: The research of the second author was supported in part by a European Advanced Grant StochExtHomog (ERC AdG 320977).
The authors are grateful for the support of the Erwin Schrödinger International Institute for Mathematical Physics at the University of Vienna, where part of this research was carried out.
Article copyright: © Copyright 2018 American Mathematical Society