Moscow Mathematical Journal

Volume 16, Issue 2, April–June 2016 pp. 381–391.

On Cohomological Equations for Suspension Flows over Vershik Automorphisms

Authors: Dmitry Zubov (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow

Summary:

In this paper we give sufficient conditions for existence of bounded solution of the cohomological equation for suspension flows over automorphisms of Markov compacta in terms of finitely additive measures, which were introduced by Bufetov. This result can be regarded as a symbolic analogue of results due to Forni and Marmi, Moussa, and Yoccoz for translation flows and interval exchange transformations.

2010 Math. Subj. Class. Primary: 37A20, Secondary: 37A05, 37B10, 37E05, 37E35, 37H15.

Keywords: Vershik automorphisms, cohomological equations, renormalization, finitely additive invariant measures, rate of convergence in the ergodic theorem, translation flows, interval exchange transformations.

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