Inducing schemes for multi-dimensional piecewise expanding maps

Peyman Eslami

doi:10.3934/dcds.2021120

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2022, Volume 42, Issue 1: 353-368. Doi: 10.3934/dcds.2021120

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Inducing schemes for multi-dimensional piecewise expanding maps

Peyman Eslami

Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy

Received: October 31, 2020

Revised: May 31, 2021

Early access: September 2021

Published: January 2022

I thank the anonymous referee for valuable suggestions. The author was supported by the European Advanced Grant StochExtHomog (ERC AdG 320977) and by the PRIN Grant Regular and stochastic behaviour in dynamical systems (PRIN 2017S35EHN)

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Abstract

We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.

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Mathematics Subject Classification: Primary: 37A25; Secondary: 37D25.

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References

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