Factoring onto $\mathbb {Z}^d$ subshifts with the finite extension property
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- by Raimundo Briceño, Kevin McGoff and Ronnie Pavlov PDF
- Proc. Amer. Math. Soc. 146 (2018), 5129-5140 Request permission
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
- Mike Boyle, Lower entropy factors of sofic systems, Ergodic Theory Dynam. Systems 3 (1983), no. 4, 541–557. MR 753922, DOI 10.1017/S0143385700002133
- Mike Boyle, Ronnie Pavlov, and Michael Schraudner, Multidimensional sofic shifts without separation and their factors, Trans. Amer. Math. Soc. 362 (2010), no. 9, 4617–4653. MR 2645044, DOI 10.1090/s0002-9947-10-05003-8
- Raimundo Briceño, The topological strong spatial mixing property and new conditions for pressure approximation, Ergodic Theory Dynam. Systems 38 (2018), no. 5, 1658–1696. MR 3819997, DOI 10.1017/etds.2016.107
- Angela Desai, A class of $\Bbb Z^d$ shifts of finite type which factors onto lower entropy full shifts, Proc. Amer. Math. Soc. 137 (2009), no. 8, 2613–2621. MR 2497473, DOI 10.1090/S0002-9939-09-09381-2
- Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995. MR 1369092, DOI 10.1017/CBO9780511626302
- Brian Marcus, Factors and extensions of full shifts, Monatsh. Math. 88 (1979), no. 3, 239–247. MR 553733, DOI 10.1007/BF01295238
- Brian Marcus and Ronnie Pavlov, Approximating entropy for a class of $\Bbb Z^2$ Markov random fields and pressure for a class of functions on $\Bbb Z^2$ shifts of finite type, Ergodic Theory Dynam. Systems 33 (2013), no. 1, 186–220. MR 3009110, DOI 10.1017/S0143385711000824
- Ronnie Pavlov and Michael Schraudner, Entropies realizable by block gluing $\Bbb {Z}^d$ shifts of finite type, J. Anal. Math. 126 (2015), 113–174. MR 3358030, DOI 10.1007/s11854-015-0014-4
- Anthony N. Quas and Paul B. Trow, Subshifts of multi-dimensional shifts of finite type, Ergodic Theory Dynam. Systems 20 (2000), no. 3, 859–874. MR 1764932, DOI 10.1017/S0143385700000468
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
- MR Author ID: 952155
- Email: kmcgoff1@uncc.edu
- Ronnie Pavlov
- Affiliation: Department of Mathematics, University of Denver, 2390 S. York Street, Denver, Colorado 80208
- MR Author ID: 845553
- Email: rpavlov@du.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5129-5140
- MSC (2010): Primary 37B50; Secondary 37B10, 37A35
- DOI: https://doi.org/10.1090/proc/14267
- MathSciNet review: 3866852