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제목 The embedding problem in topological dynamics
발표자 Gutman, Yonatan ( Institute of Mathematics, Polish Academy of Sciences ) 날짜 2018-06-29
Host KIAS Place 8309
Abstract We will give an introductory talk for a mini-course whose subject is "optimal embedding of topological dynamical systems". Given a metrizable space $X$ of dimension $d$ it is a classical fact that the minimal $n$ which guarantees that $X$ may be embedded topologically in $[0,1]^n$, is $n=2d+1$. An analogous problem in the category of dynamical systems, is under what conditions one can guarantee that a topological dynamical system $(X,T)$ embeds in $([0,1]^n)^\mathbb{Z}$ under the shift action. We will review the history of embedding problem starting from the famous Bebutov-Kakutani embedding theorem (1968) through Jaworski's theorem (1974) and Takens' delay embedding theorem (1981) culminating in the rapid developments in the last 20 years starting with Gromov's introduction of the invariant of mean dimension (1999) and the breakthrough results of Lindenstrauss and Weiss (2000). We will indicate the current state of the art and present the theorems whose proofs will be the subject of the mini-course. In particular we will present our joint result with Tusukamoto concerning optimal embedding of minimal systems (2015) whose proof offers a surprising connection to signal analysis.

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