The spacetime of a shift endomorphism

Cyr, Van; Franks, John; Kra, Bryna

doi:10.1090/tran/7254

The spacetime of a shift endomorphism
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by Van Cyr, John Franks and Bryna Kra PDF

Trans. Amer. Math. Soc. 371 (2019), 461-488 Request permission

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.

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