Book Review
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MathSciNet review:
3166046
Full text of review:
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Book Information:
Authors:
Tullio Ceccherini-Silberstein and
Michel Coornaert
Title:
Cellular automata and groups
Additional book information:
Springer Monographs in Mathematics,
Springer-Verlag,
Berlin,
2010,
xx+439 pp.,
ISBN 978-3-642-14033-4
Laurent Bartholdi, Gardens of Eden and amenability on cellular automata, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 1, 241–248. MR 2578610, DOI 10.4171/JEMS/196
Arthur W. Burks (ed.), Essays on cellular automata, University of Illinois Press, Urbana, Ill.-London, 1970. MR 0299409
Michel Coornaert and Athanase Papadopoulos, Symbolic dynamics and hyperbolic groups, Lecture Notes in Mathematics, vol. 1539, Springer-Verlag, Berlin, 1993. MR 1222644
T. G. Ceccherini-Silberstein, A. Machì, and F. Scarabotti, Amenable groups and cellular automata, Ann. Inst. Fourier (Grenoble) 49 (1999), no. 2, 673–685 (English, with English and French summaries). MR 1697376
Gábor Elek and Endre Szabó, Sofic groups and direct finiteness, J. Algebra 280 (2004), no. 2, 426–434. MR 2089244, DOI 10.1016/j.jalgebra.2004.06.023
Walter Gottschalk, Some general dynamical notions, Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Math., Vol. 318, Springer, Berlin, 1973, pp. 120–125. MR 0407821
M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109–197. MR 1694588, DOI 10.1007/PL00011162
Bruce P. Kitchens, Symbolic dynamics, Universitext, Springer-Verlag, Berlin, 1998. One-sided, two-sided and countable state Markov shifts. MR 1484730, DOI 10.1007/978-3-642-58822-8
Douglas Lind, Multi-dimensional symbolic dynamics, Symbolic dynamics and its applications, Proc. Sympos. Appl. Math., vol. 60, Amer. Math. Soc., Providence, RI, 2004, pp. 61–79. MR 2078846, DOI 10.1090/psapm/060/2078846
Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995. MR 1369092, DOI 10.1017/CBO9780511626302
Marston Morse and Gustav A. Hedlund, Symbolic Dynamics, Amer. J. Math. 60 (1938), no. 4, 815–866. MR 1507944, DOI 10.2307/2371264
C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379–423, 623–656. MR 26286, DOI 10.1002/j.1538-7305.1948.tb01338.x
Benjamin Weiss, Sofic groups and dynamical systems, Sankhyā Ser. A 62 (2000), no. 3, 350–359. Ergodic theory and harmonic analysis (Mumbai, 1999). MR 1803462
References
- Laurent Bartholdi, Gardens of Eden and amenability on cellular automata, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 1, 241–248. MR 2578610 (2011e:05282), DOI 10.4171/JEMS/196
- Arthur W. Burks (ed.), Essays on cellular automata, University of Illinois Press, Urbana, Ill., 1970. MR 0299409 (45 \#8457)
- Michel Coornaert and Athanase Papadopoulos, Symbolic dynamics and hyperbolic groups, Lecture Notes in Mathematics, vol. 1539, Springer-Verlag, Berlin, 1993. MR 1222644 (94d:58054)
- T. G. Ceccherini-Silberstein, A. Machì, and F. Scarabotti, Amenable groups and cellular automata, Ann. Inst. Fourier (Grenoble) 49 (1999), no. 2, 673–685 (English, with English and French summaries). MR 1697376 (2000k:43001)
- Gábor Elek and Endre Szabó, Sofic groups and direct finiteness, J. Algebra 280 (2004), no. 2, 426–434. MR 2089244 (2005d:16041), DOI 10.1016/j.jalgebra.2004.06.023
- Walter Gottschalk, Some general dynamical notions, Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Math., vol. 318, Springer, Berlin, 1973, pp. 120–125. MR 0407821 (53 \#11591)
- M. Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109–197. MR 1694588 (2000f:14003), DOI 10.1007/PL00011162
- Bruce P. Kitchens, Symbolic dynamics, Universitext, Springer-Verlag, Berlin, 1998. One-sided, two-sided and countable state Markov shifts. MR 1484730 (98k:58079), DOI 10.1007/978-3-642-58822-8
- Douglas Lind, Multi-dimensional symbolic dynamics, Symbolic dynamics and its applications, Proc. Sympos. Appl. Math., vol. 60, Amer. Math. Soc., Providence, RI, 2004, pp. 61–79. MR 2078846 (2005f:37038)
- Douglas Lind and Brian Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge, 1995. MR 1369092 (97a:58050), DOI 10.1017/CBO9780511626302
- Marston Morse and Gustav A. Hedlund, Symbolic Dynamics, Amer. J. Math. 60 (1938), no. 4, 815–866. MR 1507944, DOI 10.2307/2371264
- C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379–423, 623–656. MR 0026286 (10,133e)
- Benjamin Weiss, Sofic groups and dynamical systems, Sankhyā Ser. A 62 (2000), no. 3, 350–359. Ergodic theory and harmonic analysis (Mumbai, 1999). MR 1803462 (2001j:37022)
Review Information:
Reviewer:
Zoran Šunić
Affiliation:
Texas A&M University
Email:
sunic@math.tamu.edu
Journal:
Bull. Amer. Math. Soc.
51 (2014), 361-366
DOI:
https://doi.org/10.1090/S0273-0979-2013-01425-3
Published electronically:
July 23, 2013
Review copyright:
© Copyright 2013
American Mathematical Society
