The spacetime of a shift endomorphism

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4 Scopus citations

Abstract

The automorphism group of a one dimensional shift space over a finite alphabet exhibits different types of behavior: for a large class with positive entropy, it contains a rich collection of subgroups, while for many shifts of zero entropy, there are strong constraints on the automorphism group. We view this from a different perspective, considering a single automorphism (and sometimes endomorphism) and studying the naturally associated two-dimensional shift system. In particular, we describe the relation between nonexpansive subspaces in this two-dimensional system and dynamical properties of an automorphism of the shift.

Original languageEnglish (US)
Pages (from-to)461-488
Number of pages28
JournalTransactions of the American Mathematical Society
Volume371
Issue number1
DOIs
StatePublished - 2019

Keywords

  • Automorphism
  • Nonexpansive
  • Subshift

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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