February 1, 2017 at 7:00 pm

Dynamical Systems Seminar | On the Definition of Topological Entropy, Feb. 21

Ying Xin

Ying Xin

The Dynamical Systems Seminar features Ying Xin discussing “On the definition of topological entropy:  limsup (or liminf) is needed for the separation number” on Tuesday, Feb. 21, at 3:05 p.m. in Morton 226 .

SPEAKER: Ying Xin, Department of Mathematics, Ohio University

Xin is a graduate student and teaching assistant in the Mathematics Department at Ohio University.

Abstract: Entropy is a fundamental concept in the theory of dynamical systems.  The original definition was introduced by Adler, Konheim and McAndrew in 1965.  Then equivalent definitions
on compact metric spaces were introduced by Rufus  Bowen in 1971 and independently by Efim Dinaburg in 1970.  Two of these latter definitions, based on the spanning number and the separation number, are defined in terms of $\limsup$ (or $\liminf$.)

To the best of our knowledge, it has been an open problem if $\limsup$ (or $\liminf$) in these definitions can be  replaced by $\lim$.  Leading specialists believe that the answer should be negative and drop hints to this effect in standard textbooks, but no references are given and no actual counterexamples appear to be known.

This talk will present joint work of the speaker and Dr. Winfried Just:  a construction that shows that the answer is  negative for the separation number.

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