Local P entropy and stabilized automorphism groups of subshifts

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For a homeomorphism T: X→ X of a compact metric space X, the stabilized automorphism group Aut ()(T) consists of all self-homeomorphisms of X which commute with some power of T. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local P entropy. We show that when (X, T) is a non-trivial mixing shift of finite type, the local P entropy of the group Aut ()(T) is determined by the topological entropy of (X, T). We use this to give a complete classification of the isomorphism type of the stabilized automorphism groups of full shifts.

Original languageEnglish (US)
Pages (from-to)963-995
Number of pages33
JournalInventiones Mathematicae
Issue number3
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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