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Stretched-exponential mixing for $\mathscr{C}^{1+\unicode[STIX]{x1D6FC}}$ skew products with discontinuities

Published online by Cambridge University Press:  22 July 2015

PEYMAN ESLAMI
PEYMAN ESLAMI*
Affiliation:
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy email eslami@mat.uniroma2.it
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Abstract

Consider the skew product $F:\mathbb{T}^{2}\rightarrow \mathbb{T}^{2}$, $F(x,y)=(f(x),y+\unicode[STIX]{x1D70F}(x))$, where $f:\mathbb{T}^{1}\rightarrow \mathbb{T}^{1}$ is a piecewise $\mathscr{C}^{1+\unicode[STIX]{x1D6FC}}$ expanding map on a countable partition and $\unicode[STIX]{x1D70F}:\mathbb{T}^{1}\rightarrow \mathbb{R}$ is piecewise $\mathscr{C}^{1}$. It is shown that if $\unicode[STIX]{x1D70F}$ is not Lipschitz-cohomologous to a piecewise constant function on the joint partition of $f$ and $\unicode[STIX]{x1D70F}$, then $F$ is mixing at a stretched-exponential rate.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 1 , February 2017 , pp. 146 - 175
Copyright
© Cambridge University Press, 2015 

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