Exponential speed of mixing for skew-products with singularities

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.

23 pages, 3 figures

Cited by in corpus (1)

• Exponential mixing for singular skew-products