Local P entropy and stabilized automorphism groups of subshifts

2020/07/04 by Schmieding, Scott
#37B10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.02183

Abstract

For a homeomorphism T \colon 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.

Related

• Finitary Ryan's and local Q entropy for ℤ^d subshifts
• Hyperspatiality for isomorphisms of stabilized automorphism groups of shifts of finite type
• Homomorphisms to \ℝ of automorphism groups of zero entropy\n shifts
• Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups
• Entropy of local homeomorphisms with applications to infinite alphabet shift spaces