Measure-theoretic Uniformly Positive Entropy on the Space of Probability Measures

2023/05/22 by Vermersch, Rômulo M. · 1 citation
#28A33 #28D20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.13222

Abstract

For a homeomorphism T on a compact metric space X, a T-invariant Borel probability measure μ on X and a measure-theoretic quasifactor \widetildeμ of μ, we study the relationship between the local entropy of the system (X,μ,T) and of its induced system (M(X),\widetildeμ,\widetildeT), where \widetildeT is the homeomorphism induced by T on the space M(X) of all Borel probability measures defined on X.

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