Embedding minimal dynamical systems into the Hilbert cube.
Lundi, 21 Septembre, 2015 - 10:30
Résumé :
Hilbert cube is $[0,1]^Z$; the infinite product of the interval $[0,1]$. Question: Given a dynamical system, can we embed it into the shift action on the Hilbert cube? This problem has been studied more than 40 years. In the talk I will present a fairly complete answer for minimal dynamical systems. In 1999 Elon Lindenstrauss proved that minimal system of mean dimension less than $1/36$ can be embedded into the Hilbert cube. The value $1/36$ looked artificial. So he asked what is the optimal value for the embedding. Recently Yonatan Gutman and I solved this problem by proving that minimal systems of mean dimension less than $1/2$ can be embedded into the Hilbert cube. The value $1/2$ is optimal. The proof is very interesting. The nature of the above problem is purely abstract topological dynamics. But main ingredients of the proof are Fourier and complex analysis. So our work exhibits a new interaction between topological dynamics and classical analysis.
Thème de recherche :
Algèbre et géométries
Salle :
4