Disintegration of Invariant Measures for Hyperbolic Skew Products

Israel J. Math. 219 (2017) 171-188.

Oliver Butterley and Ian Melbourne

Abstract

We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable v on the skew product to an observable v on the system quotiented along stable manifolds. Under mild assumptions on the system we prove that the disintegration preserves the smoothness of v, firstly in the case where v is Höolder and secondly in the case where v is C¹.