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UID:1141@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160318T143000
DTEND;TZID=Europe/Paris:20160318T153000
DTSTAMP:20160303T133000Z
URL:https://www.i2m.univ-amu.fr/evenements/on-cohomological-equations-for-
 suspension-flows-over-vershik-automorphisms/
SUMMARY: (...): On cohomological equations for suspension flows over Vershi
 k automorphisms
DESCRIPTION:: Consider a finite oriented graph on fixed number vertices\, s
 uch that each vertex of this graph has both incoming and outgoing edges (m
 ultiple edges are permitted). An infinite sequence of such graphs can be r
 epresented as a graded graph Г. We would like to a Markov compactum -- th
 e space X of all paths in Г. The subsets of paths with the same tail at t
 he infinity form an asymptotic foliation on X. A linear ordering on the se
 ts of paths starting from each vertex of Г induces an ordering on the asy
 mptotic foliation\, linear on each leaf. There is a natural map T defined 
 on the asymptotic foliation of X\, which is called a Vershik automorphism.
  The map T take each path in X to its successor with respect to the define
 d ordering.Vershik automorphisms can be regarded as symbolic analogues of 
 various dynamical systems of parabolic type. In particular\, the interval 
 exchange maps can be realized as Vershik automorphisms of Markov compacta 
 via Rauzy-Veech induction. One more example of the Vershik automorphism is
  given by substitutional dynamics.A. Bufetov suggested considering the spe
 cial flow over Vershik automorphism\, giving a symbolic encoding of the tr
 anslation flow on flat surfaces of higher genus. He also obtained the resu
 lts about the deviation of the ergodic integral for these flows\, as well 
 as the limit theorems\, in terms of Hoelder finitely-additive measures on 
 the leaves of the asymptotic foliations.The speaker obtained\, following t
 he works of G.Forni and Marmi-Moussa-Yoccoz on translation flows and inter
 val exchange maps\, the sufficient conditions for solvability of the cohom
 ological equation for the special flow over Vershik automorphisms.Everyone
  is welcome!https://www.hse.ru/en/org/persons/165123671
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