Group extensions of Gibbs–Markov maps

Abstract

 Let φ be an aperiodic cocycles with values in a locally compact abelian second countable group ? defined on an exact Gibbs–Markov map T : X → X. We show that the group extension T _φ (x,g) = (T(x),g + φ(x)) (x ? X; g ??) is exact. Equivalent conditions for exactness are found.