A class of $\mathbb {Z}^d$ shifts of finite type which factors onto lower entropy full shifts
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- by Angela Desai PDF
- Proc. Amer. Math. Soc. 137 (2009), 2613-2621 Request permission
Abstract:
We prove that if a $\mathbb {Z}^d$ shift of finite type with entropy greater than $\log N$ satisfies the corner gluing mixing condition of Johnson and Madden, then it must factor onto the full $N$-shift.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
- Angela Desai, Subsystem entropy for $\Bbb Z^d$ sofic shifts, Indag. Math. (N.S.) 17 (2006), no. 3, 353–359. MR 2321105, DOI 10.1016/S0019-3577(06)80037-6
- Manfred Denker, Christian Grillenberger, and Karl Sigmund, Ergodic theory on compact spaces, Lecture Notes in Mathematics, Vol. 527, Springer-Verlag, Berlin-New York, 1976. MR 0457675
- Aimee Johnson and Kathleen Madden, Factoring higher-dimensional shifts of finite type onto the full shift, Ergodic Theory Dynam. Systems 25 (2005), no. 3, 811–822. MR 2142947, DOI 10.1017/S0143385704000823
- Wolfgang Krieger, On the subsystems of topological Markov chains, Ergodic Theory Dynam. Systems 2 (1982), no. 2, 195–202 (1983). MR 693975, DOI 10.1017/S0143385700001516
- Samuel J. Lightwood, Morphisms from non-periodic $\Bbb Z^2$-subshifts. I. Constructing embeddings from homomorphisms, Ergodic Theory Dynam. Systems 23 (2003), no. 2, 587–609. MR 1972240, DOI 10.1017/S014338570200130X
- Samuel J. Lightwood, Morphisms from non-periodic $\Bbb Z^2$ subshifts. II. Constructing homomorphisms to square-filling mixing shifts of finite type, Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1227–1260. MR 2085910, DOI 10.1017/S0143385704000276
- 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
- E. Arthur Robinson Jr. and Ayşe A. Şahin, Modeling ergodic, measure preserving actions on $\Bbb Z^d$ shifts of finite type, Monatsh. Math. 132 (2001), no. 3, 237–253. MR 1844076, DOI 10.1007/s006050170043
Additional Information
- Angela Desai
- Affiliation: Department of Biology, Chemistry, and Mathematics, University of Montevallo, Montevallo, Alabama 35115
- Address at time of publication: Department of Mathematics, Anne Arundel Community College, 101 College Parkway, Arnold, Maryland 21012
- Email: avdesai@aacc.edu
- Received by editor(s): March 28, 2007
- Received by editor(s) in revised form: September 22, 2007
- Published electronically: March 25, 2009
- Communicated by: Jane M. Hawkins
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2613-2621
- MSC (2000): Primary 37B10; Secondary 37B40
- DOI: https://doi.org/10.1090/S0002-9939-09-09381-2
- MathSciNet review: 2497473