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.References
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Additional Information
- Van Cyr
- Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
- MR Author ID: 883244
- Email: van.cyr@bucknell.edu
- John Franks
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- MR Author ID: 68865
- Email: j-franks@northwestern.edu
- Bryna Kra
- Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
- MR Author ID: 363208
- ORCID: 0000-0002-5301-3839
- Email: kra@math.northwestern.edu
- Received by editor(s): November 1, 2016
- Received by editor(s) in revised form: February 28, 2017, April 5, 2017, and April 6, 2017
- Published electronically: June 20, 2018
- Additional Notes: The third author was partially supported by NSF grant 1500670.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 461-488
- MSC (2010): Primary 37B10; Secondary 37B15, 54H20
- DOI: https://doi.org/10.1090/tran/7254
- MathSciNet review: 3885151