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SUMMARY:Title to be confirmed - Speaker to be confirmed
DTSTART:20121009T100000Z
DTEND:20121009T110000Z
UID:TALK40951@talks.cam.ac.uk
CONTACT:Yonatan Gutman
DESCRIPTION:<PRE> According to the celebrated Jaworski Theorem\, a finite 
 dimensional aperiodic dynamical system $(X\,T)$ embeds in the $1$-dimensio
 nal cubical shift $([0\,1]{}}\,shift)$. If $X$ admits periodic points (sti
 ll assuming $dim(X)<\\infty$) then we show that periodic dimension $perdim
 (X\,T)<\\frac{d}{2}$ implies that $(X\,T)$ embeds in the $d$-dimensional c
 ubical shift $(([0\,1]{d})}\,shift)$. This verifies a conjecture by Linden
 strauss and Tsukamoto for finite dimensional systems. Moreover for an infi
 nite dimensional dynamical system\, with the same periodic dimension assum
 ption\, the set of periodic points can be equivariantly immersed in $(([0\
 ,1]{d})}\,shift)$. Furthermore we introduce a notion of (Krieger) markers 
 for general topological dynamical systems\, and use a generalized version 
 of the Bonatti-Crovisier Tower Theorem\, to show that an extension $(X\,T)
 $ of an aperiodic finite-dimensional system whose mean dimension obeys $md
 im(X\,T)<\\frac{d}{16}$ embeds in the \\textit{$(d+1)$-}cubical shift $(([
 0\,1]{d+1})}\,shift)$. Finally we compare these results to a recent sharp 
 theorem joint with Tsukamoto: If $(X\,T)$ is an extension of an aperiodic 
 subshift and its mean dimension verifies $mdim(X\,T)<\\frac{d}{2}$ then it
  embeds in the $d$-dimensional cubical shift $(([0\,1]{d})^{\\mathbb{Z}}\,
 shift)$.<\\PRE>
LOCATION:Venue to be confirmed
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