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UID:4173@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20160318T143000
DTEND;TZID=Europe/Paris:20160318T153000
DTSTAMP:20160303T133000Z
URL:https://www.i2m.univ-amu.fr/events/on-cohomological-equations-for-susp
ension-flows-over-vershik-automorphisms/
SUMMARY:On cohomological equations for suspension flows over Vershik automo
rphisms -
DESCRIPTION:Consider a finite oriented graph on fixed number vertices\, suc
h that each vertex of this graph has both incoming and outgoing edges (mul
tiple edges are permitted). An infinite sequence of such graphs can be rep
resented as a graded graph Г. We would like to a Markov compactum -- the
space X of all paths in Г. The subsets of paths with the same tail at the
infinity form an asymptotic foliation on X. A linear ordering on the sets
of paths starting from each vertex of Г induces an ordering on the asymp
totic foliation\, linear on each leaf. There is a natural map T defined on
the asymptotic foliation of X\, which is called a Vershik automorphism. T
he map T take each path in X to its successor with respect to the defined
ordering.Vershik automorphisms can be regarded as symbolic analogues of va
rious dynamical systems of parabolic type. In particular\, the interval ex
change maps can be realized as Vershik automorphisms of Markov compacta vi
a Rauzy-Veech induction. One more example of the Vershik automorphism is g
iven by substitutional dynamics.A. Bufetov suggested considering the speci
al flow over Vershik automorphism\, giving a symbolic encoding of the tran
slation flow on flat surfaces of higher genus. He also obtained the result
s about the deviation of the ergodic integral for these flows\, as well as
the limit theorems\, in terms of Hoelder finitely-additive measures on th
e leaves of the asymptotic foliations.The speaker obtained\, following the
works of G.Forni and Marmi-Moussa-Yoccoz on translation flows and interva
l exchange maps\, the sufficient conditions for solvability of the cohomol
ogical equation for the special flow over Vershik automorphisms.Everyone i
s welcome!https://www.hse.ru/en/org/persons/165123671
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