Exponential mixing for skew products with discontinuities

Butterley, Oliver; Eslami, Peyman

doi:10.1090/tran/6761

Exponential mixing for skew products with discontinuities
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by Oliver Butterley and Peyman Eslami PDF

Trans. Amer. Math. Soc. 369 (2017), 783-803 Request permission

Abstract:

We consider the 2D skew product $F: (x,u) \mapsto (f(x), u+\tau (x))$, where the base map $f$ is a piecewise $\mathscr {C}^{2}$, covering and uniformly expanding the map of the circle, and the fibre map $\tau$ is piecewise $\mathscr {C}^{2}$. We show that this system mixes exponentially when $\tau$ is not cohomologous (via a Lipschitz function) to a piecewise constant.

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