For amenable group actions, IE-tuples of the induced measure system equal the closed convex hull of IE-tuples of the original system, with partial analogues for IN and IT tuples and a sharp n ≤ C log m embedding bound for ℓ_q^n inside ℓ_∞^m.
Local entropy theory and applications
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This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
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Local entropy theory, combinatorics, and local theory of Banach spaces
For amenable group actions, IE-tuples of the induced measure system equal the closed convex hull of IE-tuples of the original system, with partial analogues for IN and IT tuples and a sharp n ≤ C log m embedding bound for ℓ_q^n inside ℓ_∞^m.