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{\Large Department of Mathematics, BGU}

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{\Huge Probability and ergodic theory (PET)}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, January 17, 2017}
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\textbf{At} \emph{10:50 -- 12:00}
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\textbf{In} \emph{Math -101}

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{\large\scshape Tom Meyerovitch}
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will talk about
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{\Large\bfseries Entropy, Asymptotic pairs and Pseudo-Orbit Tracing for actions of amenable groups\par}
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\textsc{Abstract:}
Chung and Li {[}Invent. Math. 2015{]} proved that for every  expansive action of a countable polycyclic-by-finite group
$\Gamma$ on a compact group $X$ by continuous group automorphisms, positive entropy
implies the existence of non-diagonal  asymptotic pairs.
In the same paper they asked if the this holds in general for an expansive  action of a countable
amenable group $\Gamma$ on a compact space $X$.

In my talk I plan to explain the notions involved Chung and Li's question and discuss a  property of dynamical systems called the ``pseudo-orbit tracing property'{}'. R. Bowen introduced the pseudo-orbit tracing property in the 1970's for $\mathbb{Z}$-actions while studying Axiom A maps. I will prove that Chung and Li's question has an affirmative answer if one also assumes  pseudo-orbit tracing, and explain implications for algebraic actions (automorphisms of compact abelian groups).

I  will also  explain why the answer to Chung and Li's question is negative if one doesn't assume the pseudo-orbit tracing property, even when the acting group is $\mathbb{Z}$, or when the action is algebraic (but not both).








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