Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure

Ian Melbourne; Dalia Terhesiu

doi:10.3934/jmd.2018011

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2018, Volume 12: 285-313. Doi: 10.3934/jmd.2018011

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Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure

Ian Melbourne^1, and
Dalia Terhesiu^2,

1.
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
2.
Mathematics Department, University of Exeter, EX4 4QF, UK

Received: November 30, 2015

Revised: April 28, 2018

Published: October 2018

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We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgo-pyat-type condition on nonexistence of approximate eigenfunctions, we prove that existing results for (possibly non-Markovian) nonuniformly expanding maps hold also for their toral extensions.

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Mathematics Subject Classification: Primary: 37A25; Secondary: 37A40, 37D25, 60K05.

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