TY - JOUR
T1 - Local P entropy and stabilized automorphism groups of subshifts
AU - Schmieding, Scott
N1 - Funding Information:
The author would like to thank Bryna Kra for several helpful conversations related to the contents of this paper, and is very grateful to Mike Boyle for numerous suggestions which improved the paper.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85117723922&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85117723922&partnerID=8YFLogxK
U2 - 10.1007/s00222-021-01076-8
DO - 10.1007/s00222-021-01076-8
M3 - Article
AN - SCOPUS:85117723922
SN - 0020-9910
VL - 227
SP - 963
EP - 995
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -