Local entropy theory, combinatorics, and local theory of Banach spaces

2025/07/04 by Li, Hanfeng, Liu, Kairan · 2 citations
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.03338

Abstract

Each continuous action of a countably infinite discrete group Γ on a compact metrizable space X induces a continuous action of Γ on the space M(X) of Borel probability measures on X. We compare the local entropy theory for these two actions, and describe the relation between their IE-tuples. Several other types of tuples are also studied. Our main tool is a new combinatorial lemma. We also give an application of the combinatorial lemma to the local theory of Banach spaces.

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