Cohomological equations for suspension flows over Vershik automorphisms

TL;DR

This paper establishes conditions for solving cohomological equations in suspension flows over Vershik automorphisms, extending symbolic dynamics analogues of classical results in translation flows and interval exchanges.

Contribution

It provides sufficient conditions for the existence of solutions to cohomological equations in a new symbolic setting involving Vershik automorphisms.

Findings

Derived conditions ensure solvability of cohomological equations

Extended classical results to symbolic automorphism flows

Bridged symbolic dynamics with geometric flow theories

Abstract

In this paper we give sufficient conditions for existence of a solution of cohomological equation for suspension flows over automorphisms of Markov compacta, which were introduced by Vershik and Ito. The main result (Theorem 1) can be regarded as a symbolic analogue of results due to Forni and Marmi, Moussa and Yoccoz for translation flows and interval exchange transformations.