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On spatial entropy of multi-dimensional symbolic dynamical systems
1. | College of Mathematics, Sichuan University, Chengdu 610064, China |
2. | Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300 |
References:
[1] |
P. Ballister, B. Bollobás and A. Quas, Entropy Along Convex Shapes, Random Tilings and Shifts of Finite Type, Illinois journal of Matlaematics, 46 (2002), 781-795. |
[2] |
J. C. Ban, W. G. Hu, S. S. Lin and Y. H. Lin, Zeta functions for two-dimensional shifts of finite type, Memo. Amer. Math. Soc., 221 (2013), vi+60 pp.
doi: 10.1090/S0065-9266-2012-00653-8. |
[3] |
J. C. Ban, W. G. Hu, S. S. Lin and Y. H. Lin, Verification of mixing properties in two-dimensional shifts of finite type, submitted,, , ().
|
[4] |
J. C. Ban and S. S. Lin, Patterns generation and transition matrices in multi-dimensional lattice models, Discrete Contin. Dyn. Syst., 13 (2005), 637-658.
doi: 10.3934/dcds.2005.13.637. |
[5] |
J. C. Ban, S. S. Lin and Y. H. Lin, Patterns generation and spatial entropy in two dimensional lattice models, Asian J. Math., 11 (2007), 497-534.
doi: 10.4310/AJM.2007.v11.n3.a7. |
[6] |
K. Böröczky Jr., M. A. Hernández Cifre and G. Salinas, Optimizing area and perimeter of convex sets for fixed circumradius and inradius, Monatsh. Math., 138 (2003), 95-110.
doi: 10.1007/s00605-002-0486-z. |
[7] |
M. Boyle, R. Pavlov and M. Schraudner, Multidimensional sofic shifts without separation and their factors, Trans. Amer. Math. Soc., 362 (2010), 4617-4653.
doi: 10.1090/S0002-9947-10-05003-8. |
[8] |
G. D. Chakerian and S. K. Stein, Some intersection properties of convex bodies, Proc. Amer. Math. Soc., 18 (1967), 109-112.
doi: 10.1090/S0002-9939-1967-0206818-3. |
[9] |
S. N. Chow, J. Mallet-Paret and E. S. Van Vleck, Pattern formation and spatial chaos in spatially discrete evolution equations, Random Comput. Dynam., 4 (1996), 109-178. |
[10] |
M. Hochman and T. Meyerovitch, A characterization of the entropies of multidimensional shifts of finite type, Annals of Mathematics, 171 (2010), 2011-2038.
doi: 10.4007/annals.2010.171.2011. |
[11] |
W. G. Hu and S. S. Lin, Nonemptiness problems of plane square tiling with two colors, Proc. Amer. Math. Soc., 139 (2011), 1045-1059.
doi: 10.1090/S0002-9939-2010-10518-X. |
[12] |
W. Huang, X. D. Ye and G. H. Zhang, Local entropy theory for a countable discrete amenable group action, J. Funct. Anal., 261 (2011), 1028-1082.
doi: 10.1016/j.jfa.2011.04.014. |
[13] |
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
[14] |
E. Lindenstrauss and B. Weiss, Mean topological dimension, Israel J. Math., 115 (2000), 1-24.
doi: 10.1007/BF02810577. |
[15] |
N. G. Markley and M. E. Paul, Maximal measures and entropy for $Z^{\nu}$ subshift of finite type, Classical Mechanics and Dynamical Systems, Lecture Notes in Pure and Appl. Math., 70 (1981), 135-157. |
[16] |
N. G. Markley and M. E. Paul, Matrix subshifts for $Z^{\nu }$ symbolic dynamics, Proc. London Math. Soc., 43 (1981), 251-272.
doi: 10.1112/plms/s3-43.2.251. |
[17] |
P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4612-5775-2. |
show all references
References:
[1] |
P. Ballister, B. Bollobás and A. Quas, Entropy Along Convex Shapes, Random Tilings and Shifts of Finite Type, Illinois journal of Matlaematics, 46 (2002), 781-795. |
[2] |
J. C. Ban, W. G. Hu, S. S. Lin and Y. H. Lin, Zeta functions for two-dimensional shifts of finite type, Memo. Amer. Math. Soc., 221 (2013), vi+60 pp.
doi: 10.1090/S0065-9266-2012-00653-8. |
[3] |
J. C. Ban, W. G. Hu, S. S. Lin and Y. H. Lin, Verification of mixing properties in two-dimensional shifts of finite type, submitted,, , ().
|
[4] |
J. C. Ban and S. S. Lin, Patterns generation and transition matrices in multi-dimensional lattice models, Discrete Contin. Dyn. Syst., 13 (2005), 637-658.
doi: 10.3934/dcds.2005.13.637. |
[5] |
J. C. Ban, S. S. Lin and Y. H. Lin, Patterns generation and spatial entropy in two dimensional lattice models, Asian J. Math., 11 (2007), 497-534.
doi: 10.4310/AJM.2007.v11.n3.a7. |
[6] |
K. Böröczky Jr., M. A. Hernández Cifre and G. Salinas, Optimizing area and perimeter of convex sets for fixed circumradius and inradius, Monatsh. Math., 138 (2003), 95-110.
doi: 10.1007/s00605-002-0486-z. |
[7] |
M. Boyle, R. Pavlov and M. Schraudner, Multidimensional sofic shifts without separation and their factors, Trans. Amer. Math. Soc., 362 (2010), 4617-4653.
doi: 10.1090/S0002-9947-10-05003-8. |
[8] |
G. D. Chakerian and S. K. Stein, Some intersection properties of convex bodies, Proc. Amer. Math. Soc., 18 (1967), 109-112.
doi: 10.1090/S0002-9939-1967-0206818-3. |
[9] |
S. N. Chow, J. Mallet-Paret and E. S. Van Vleck, Pattern formation and spatial chaos in spatially discrete evolution equations, Random Comput. Dynam., 4 (1996), 109-178. |
[10] |
M. Hochman and T. Meyerovitch, A characterization of the entropies of multidimensional shifts of finite type, Annals of Mathematics, 171 (2010), 2011-2038.
doi: 10.4007/annals.2010.171.2011. |
[11] |
W. G. Hu and S. S. Lin, Nonemptiness problems of plane square tiling with two colors, Proc. Amer. Math. Soc., 139 (2011), 1045-1059.
doi: 10.1090/S0002-9939-2010-10518-X. |
[12] |
W. Huang, X. D. Ye and G. H. Zhang, Local entropy theory for a countable discrete amenable group action, J. Funct. Anal., 261 (2011), 1028-1082.
doi: 10.1016/j.jfa.2011.04.014. |
[13] |
D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511626302. |
[14] |
E. Lindenstrauss and B. Weiss, Mean topological dimension, Israel J. Math., 115 (2000), 1-24.
doi: 10.1007/BF02810577. |
[15] |
N. G. Markley and M. E. Paul, Maximal measures and entropy for $Z^{\nu}$ subshift of finite type, Classical Mechanics and Dynamical Systems, Lecture Notes in Pure and Appl. Math., 70 (1981), 135-157. |
[16] |
N. G. Markley and M. E. Paul, Matrix subshifts for $Z^{\nu }$ symbolic dynamics, Proc. London Math. Soc., 43 (1981), 251-272.
doi: 10.1112/plms/s3-43.2.251. |
[17] |
P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982.
doi: 10.1007/978-1-4612-5775-2. |
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