Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Factoring onto $ \mathbb{Z}^d$ subshifts with the finite extension property


Authors: Raimundo Briceño, Kevin McGoff and Ronnie Pavlov
Journal: Proc. Amer. Math. Soc. 146 (2018), 5129-5140
MSC (2010): Primary 37B50; Secondary 37B10, 37A35
DOI: https://doi.org/10.1090/proc/14267
Published electronically: September 10, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We define the finite extension property for $ d$-dimensional subshifts, which generalizes the topological strong spatial mixing condition defined by the first author, and we prove that this property is invariant under topological conjugacy. Moreover, we prove that for every $ d$, every $ d$-dimensional block gluing subshift factors onto every $ d$-dimensional shift of finite type with strictly lower entropy, a fixed point, and the finite extension property. This result extends a theorem from [Trans. Amer. Math. Soc. 362 (2010), 4617-4653], which requires that the factor contain a safe symbol.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37B50, 37B10, 37A35

Retrieve articles in all journals with MSC (2010): 37B50, 37B10, 37A35


Additional Information

Raimundo Briceño
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email: raimundob@mail.tau.ac.il

Kevin McGoff
Affiliation: Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
Email: kmcgoff1@uncc.edu

Ronnie Pavlov
Affiliation: Department of Mathematics, University of Denver, 2390 S. York Street, Denver, Colorado 80208
Email: rpavlov@du.edu

DOI: https://doi.org/10.1090/proc/14267
Keywords: $\mathbb{Z}^d$, shift of finite type, block gluing, factor map
Received by editor(s): November 9, 2016
Received by editor(s) in revised form: January 13, 2017, and October 16, 2017
Published electronically: September 10, 2018
Additional Notes: The first author acknowledges the support of ERC Starting Grants 678520 and 676970.
The second author acknowledges the support of NSF grant DMS-1613261.
The third author acknowledges the support of NSF grant DMS-1500685.
Communicated by: Nimish Shah
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society