Classification problems for shifts on modules over a principal ideal domain

Transactions of the American Mathematical Society

Volumn 349, Issue 5, 1997, Pages 1993-2006

  Fagnani, Fabio ^a   Zampieri, Sandro ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Behavioral approach; Dynamical systems; Polynomial matrices; Principal ideal domains; Shifts; Transitivity

Indexed keywords

EID: 21744458666     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01876-x     Document Type: Article

References (23)

1. F. Blanchard. Systèmes dynamiques topologiques associés àdes automates récurrents. Z. Wahr. Verw. Geb., 58 (1981), 549-564. MR 83c:68101
2. F. Blanchard, G. Hansel. Systèmes codés. Theoretical Computer Science, 44 (1986), 17-49. MR 871:93002
3. W. Brewer, J.W. Bunce, and F.S. Van Vleck. Linear systems over commutative rings. Dekker, 1986
4. E.E. Dinaburg. An example of the computation of topological entropy. Uspehi Mat. Nauk., 23 (1968), 249-250. MR 37:5883
5. F. Fagnani. Some results on the classification of expansive automorphisms of compact Abelian groups. Ergodic Theory and Dynamical Systems, 16 (1996), 45-50. CMP 96:8
6. F. Fagnani. Shifts on compact and discrete Lie groups: algebraic-topological invariants and classification problems. To appear in Advances in Mathematics
7. G.D. Forney and M.D. Trott. The dynamics of group codes: State spaces, trellis diagrams and canonical encoders. IEEE Trans, on Information Theory, IT-39 (1993), 1491-1513. MR 96e:94017
8. P. Fuhrmann Linear systems and operators in Hubert spaces. McGraw-Hill, New York, 1981. MR 83d:47001
9. B.P. Kitchens. Expansive dynamics on zero-dimensional groups. Ergodic Theory and Dynamical Systems, 7 (1987), 249-261. MR 88i:28039
10. B.P. Kitchens and K. Schmidt. Automorphisms of compact groups. Ergodic Theory and Dynamical Systems, 9 (1989), 691-735. MR 91g:22008
11. W. Krieger. On the uniqueness of the equilibrium state. Math. Systems Theory, 8 (1974), 97-104. MR 53:3256
12. S. Kung, B. Levy, M. Morf, and T. Kailath. New results in 2D systems theory. Part 1. Proc IEEE, 65 (1977), 861-872
13. T.Y Lam, Serre's conjecture Springer LNM 635, 1978. MR 58:5644
14. B. Levy. 2D polynomial and rational matrices, and their applications for the modelling o 2D dynamical systems. Technical Report M735-11, Stanford Electronics Lab., 1981.
15. I.G. MacDonald. Duality over complete local rings. Topology, 1 (1962), 213-235. MR 27:1476
16. G. Miles and R.K. Thomas. The breakdown of automorphisms of compact topological groups In G.C. Rota, editor, Studies in Probability and Ergodic Theory, 207-218. Academic Press 1978. MR 80c:22007
17. K. Petersen. Chains, entropy, coding. Ergodic Theory Dynamical Systems, 6 (1986), 415-448 MR 88i:28040
18. I.A. Salama. Topological entropy and recurrence of countable chains. Pacific J. Math., 134 (1988), 325-341; errata: Pacific J. Math., 140 (1989), 397-398. MR 90d:54076; M 90k:54055
19. K. Schmidt. Automorphisms of compact Abelian groups and affine varieties. Proc. Londo Math. Soc. 61 (1990), 480-496. MR 91j:28015
20. E.D. Sontag. Linear systems over commutative rings: A survey. Ricerche di Automatica, 7 (1976), 1-34
21. J.C. Willems. Models for dynamics. Dynamics Reported, 2 (1988), 171-269. MR 90g:58121
22. S. Zampieri and S.K. Mitter. Linear systems over Noetherian rings in the behavioural approach. Journal of Mathematical Systems, Estimation, and Control, 6 (1996), 235-238.
23. D. Zelinsky. Linearly compact modules and rings. Amer. J. Math., 75 (1953), 79-90. M 14:532 SCUOLA