An introduction to naive entropy

Speaker: 
Dominik Kwietniak
Date: 
Tue, Apr 28, 2020
Location: 
Zoom
Conference: 
CRG: 
Abstract: 

There are simple formulas defining "naive entropy" for continuous/measure preserving actions of a countable group G on a compact metric/probability space. It turns out that if G is amenable, then this naive entropy coincides with topological/Kolmogoro-Sinai entropy of the action, while for non-amenable groups both naive entropies take only two values: 0 or infinity. During my talk, I will try to sketch the proofs of these facts. I will follow: T. Downarowicz, B. Frej, P.-P. Romagnoli, Shearer's inequality and infimum rule for Shannon entropy and topological entropy. Dynamics and numbers, 63-75, Contemp. Math., 669, Amer. Math. Soc., Providence, RI, 2016. MR3546663 and P. Burton, Naive entropy of dynamical systems. Israel J. Math. 219 (2017), no. 2, 637-659. MR3649602.

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