Ying Xin
Dr. Winfried Just and graduate student Ying Xin present a seminar titled “On the role of limsup in definitions of topological entropy: What we proved, how we proved it, and what remains open” on Tuesday, Sept. 26, from 3:05 to 4 p.m. in Morton 218.
Winfried is Professor of Mathematics at Ohio University. Xin is a graduate student and Teaching Assistant in Mathematics.
Abstract: This talk aims at giving an accessible presentation of recent results by the speakers. Topological entropy is a fundamental characteristic of a dynamical system that measures its complexity. Two of the standard definitions of this notions, based on so-called separation numbers and spanning numbers, respectively, involve a limit superior. There has been a broad consensus that this limit superior cannot be replaced by a limit. But what is the evidence? The definitions date back to around 1970, but until this year, no specific counterexamples were known. An example that shows necessity of the limit superior in the definition based on separation numbers was constructed by us early this year and presented in this seminar by Ying Xin. Subsequently we proved the analogous result for the definition based on spanning numbers. In this talk we will focus on discussing the main ideas of these constructions.
Dr. Winfried Just
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