Institute of Mathematics for Industry

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Symbolic extensions on surfaces in intermediate smoothness


Hold Date 2011-09-16 15:00~2011-09-16 18:00

Place seminar room 6, Faculty of Mathematics building, Ito Campus

Object person  

Speaker David Burguet (Ecole Normale Superieure Cachan (France))

summary:
By a symbolic extension of a topological dynamical system (X,T)
we mean an extension of (X,T) which is a subshift over a finite alphabet.
The existence and the entropy of these extensions are related to the
convergence of the entropy of (X,T) computed at finer and finer scales.
T.Downarowicz and S.Newhouse have conjectured that any C^r map,
with 1<r<+\infty, on a compact manifold admits symbolic extensions.
In this talk I will discuss the case of surface maps. In particular I
will explain how Yomdin's theory allows to estimate the infimum of the
entropy of these extensions in terms of the smoothness and the Lyapunov
exponents.