Free ergodic $\mathbb {Z}^2$-systems and complexity
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- by Van Cyr and Bryna Kra PDF
- Proc. Amer. Math. Soc. 145 (2017), 1163-1173 Request permission
Abstract:
Using results relating the complexity of a two dimensional subshift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on $[0,1)$ which is invariant under both $x\mapsto px \pmod 1$ and $x\mapsto qx \pmod 1$, showing that any potential counterexample has a nontrivial lower bound on its complexity.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
- 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): January 25, 2016
- Received by editor(s) in revised form: May 5, 2016
- Published electronically: September 15, 2016
- Additional Notes: The second author was partially supported by NSF grant 1500670.
- Communicated by: Nimish Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1163-1173
- MSC (2010): Primary 28D05, 37A25, 37A35
- DOI: https://doi.org/10.1090/proc/13279
- MathSciNet review: 3589316