Two-sided shift spaces over infinite alphabets

Abstract

Ott, Tomforde, and Willis proposed a useful compactification for one-sided shifts over infinite alphabets. Building from their idea we develop a notion of two-sided shift spaces over infinite alphabets, with an eye towards generalizing a result of Kitchens. As with the one-sided shifts over infinite alphabets our shift spaces are compact Hausdorff spaces but, in contrast to the one-sided setting, our shift map is continuous everywhere. We show that many of the classical results from symbolic dynamics are still true for our two-sided shift spaces. In particular, while for one-sided shifts the problem about whether or not any $M$-step shift is conjugate to an edge shift space is open, for two-sided shifts we can give a positive answer for this question.

32 pages

References in corpus (6)

• Graph inverse semigroups, groupoids and their C*-algebras
• Sliding block codes between shift spaces over infinite alphabets
• Markov Towers and Stochastic Properties of Billiards
• A note on the definition of sliding block codes and the Curtis-Hedlund-Lyndon Theorem
• Inverse semigroup shifts over countable alphabets
• (M + 1)-step shift spaces that are not conjugate to M-step shift spaces

Cited by in corpus (6)

• Sliding block codes between shift spaces over infinite alphabets
• A note on the definition of sliding block codes and the Curtis-Hedlund-Lyndon Theorem
• Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts
• Inverse semigroup shifts over countable alphabets
• The socle of subshift algebras, with applications to subshift conjugacy
• Ultragraphs and shifts spaces over infinite alphabets