Central Limit theorem and cohomological equation on homogeneous space

Ronggang Shi

Published 2018-12-10Version 1

The dynamics of one parameter diagonal group action on finite volume homogeneous space has a partially hyperbolic nature. In this paper we extend the Livsic type result on measurable rigidity to this possibly noncompact system. We also prove a central limit theorem for the Birkhoff averages of points on a horospherical orbit. The measurable rigidity result allows us to show that the variance of the central limit theorem is nonzero provided that the test function has nonzero mean with respect to an invariant probability measure.