Stretched-exponential mixing for ${\mathcal{C}}^{1+\alpha }$ skew products with discontinuities

Abstract

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

21 pages

References in corpus (2)

• Exponential decay of correlations for piecewise cone hyperbolic contact flows
• Area expanding C^{1+α} Suspension Semiflows

Cited by in corpus (1)

• Exponential mixing for singular skew-products