The spacetime of a shift endomorphism

Research output: Contribution to journalArticle

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 - Jan 1 2019

Fingerprint

Endomorphism
Automorphism
Automorphism Group
Entropy
Space-time
Two-dimensional Systems
Subspace
Subgroup
Zero
Class

Keywords

  • Automorphism
  • Nonexpansive
  • Subshift

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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The spacetime of a shift endomorphism. / Cyr, Van; Franks, John M; Kra, Bryna R.

In: Transactions of the American Mathematical Society, Vol. 371, No. 1, 01.01.2019, p. 461-488.

Research output: Contribution to journalArticle

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