The automorphism group of a shift of finite type

Transactions of the American Mathematical Society

Volumn 306, Issue 1, 1988, Pages 71-114

  Boyle, Mike ^a   Lind, Douglas ^a   Rudolph, Daniel ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84956252003     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-1988-0927684-2     Document Type: Article

References (37)

1. R. Adler, D. Coppersmith, and M. Hassner, Algorithms for sliding block codes, IEEE Trans, on Information Theory 29 (1983), 5-22.
2. R. Bowen, Topological entropy and Axiom A, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 23-41.
3. M. Boyle, Lower entropy factors of sofic systems, Ergodic Theory Dynamical Systems 4 (1984), 541-557.
4. M. Boyle, Shift equivalence and the Jordan form away from zero, Ergodic Theory Dynamical Systems 4 (1984), 367-379.
5. M. Boyle and W. Krieger, Periodic points and automorphisms of the shift, Trans. Amer. Math. Soc. 302 (1987), 125-149.
6. M. Boyle, B. Marcus, and P. Trow, Resolving maps and the dimension group for shifts of finite type, Mem. of Amer. Math. Soc. (to appear).
7. A. Brumer, On the units of algebraic number fields, Mathematika 14 (1967), 121-124.
8. E. Coven, Endomorphisms of substitutions minimal sets, Z. Wahrsch. Verw. Gebiete. 20 (1971), 129-133.
9. E. Coven and M. Keane, The structure of substitution minimal sets, Trans. Amer. Math. Soc. 162 (1971), 89-102.
10. E. Coven and M. Paul, Endomorphisms of irreducible subshifts of finite type, Math. Systems Theory 8 (1974), 167-175.
11. M. Denker, C. Grillenberger, and K. Sigmund, Ergodic theory on compact spaces, Lecture Notes in Math., vol. 527, Springer, New York, 1976.
12. G. A. Elliott, On the classification of inductive limits of sequences of semisimple finite-dimensional algebras, J. Algebra 38 (1976), 29-44.
13. E. Gilbert, Synchronization of binary messages, IRE Trans. Inform. Theory 6 (1960), 470-477.
14. G. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320-375.
15. I. Kaplansky, Infinite Abelian groups, University of Michigan Press, Ann Arbor, 1954.
16. N. Koblitz, p-adic numbers, p-adic analysis, and zeta-functions, Springer, New York, 1977.
17. W. Krieger, On the subsystems of topological Markov chains, Ergodic Theory Dynamical Systems 2 (1982), 195-202.
18. W. Krieger, On dimension functions and topological Markov chains, Invent. Math. 56 (1980), 239-250.
19. D. Lind, The entropies of topological Markov shifts and a related class of algebraic integers, Ergodic Theory Dynamical Systems 4 (1984), 283-300.
20. D. Lind, Entropies of automorphisms of a topological Markov shift, Proc. Amer. Math. Soc. (to appear).
21. R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Ergebnisse der Math. 89, Springer, Heidelberg, 1977.
22. W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory, Dover, New York, 1976.
23. M. Nasu, Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts, Proc. Univ. Maryland Special Year in Dynamical Systems 1986-87, Springer (to appear).
24. W. Parry and S. Tuncel, Classification problems in ergodic theory, London Math. Soc. Lecture Notes 67, Cambridge University Press, Cambridge, 1982.
25. J. Rotman, The theory of groups, Allyn and Bacon, Boston, Mass., 1973.
26. J. Ryan, The shift and commutativity, Math. Systems Theory 6 (1972), 82-85.
27. J. Ryan, The shift and commutativity II, Math. Systems Theory 8 (1974), 249-250.
28. M. Sears, The automorphisms of the shift dynamical system are relatively sparse, Math. Systems Theory 5 (1971), 228-231.
29. P. Shields, The theory of Bernoulli shifts, Univ. of Chicago Press, Chicago, 1973.
30. S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817.
31. O. Taussky, On a theorem of Latimer and MacDuffee, Can ad. J. Math. 1 (1949), 300-302.
32. J. Wagoner, Realizing symmetries of a subshift of finite type by homeomorphisms of spheres, Bull. Amer. Math. Soc. 14 (1986), 301-03.
33. J. Wagoner, Markov partitions and Ki, preprint, Univ. of California, Berkeley, 1985.
34. P. Walters, An introduction to ergodic theory, Springer, New York, 1982.
35. E. Weiss, Algebraic number theory, McGraw-Hill, New York, 1963.
36. R. Williams, Classification of subshifts of finite type, Ann. of Math. 98 (1973), 120-153; Errata
37. R. Williams, Classification of subshifts of finite type 99 (1974) 380-381.