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arXiv · 1202.2162

Exponential speed of mixing for skew-products with singularities

R. Markarian·M. J. Pacifico·J. Vieitez
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Abstract

Let $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the $C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.

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R. Markarian, M. J. Pacifico, J. Vieitez. 2012-02-10. Exponential speed of mixing for skew-products with singularities. https://doi.org/10.1088/0951-7715%2F26%2F1%2F269

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