We study skew-products of the form (x,u) bar right arrow (fx,u+phi(x)) where f is a non-uniformly expanding map on a manifold X and phi:X -> S1 is piecewise C1. If the systems satisfies mild assumptions (in particular singular behaviour of phi is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map.
Butterley, O. (2024). Exponential mixing for singular skew-products. NONLINEARITY, 37(11) [10.1088/1361-6544/ad8333].
Exponential mixing for singular skew-products
Butterley, Oliver
2024-01-01
Abstract
We study skew-products of the form (x,u) bar right arrow (fx,u+phi(x)) where f is a non-uniformly expanding map on a manifold X and phi:X -> S1 is piecewise C1. If the systems satisfies mild assumptions (in particular singular behaviour of phi is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map.File in questo prodotto:
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