Geodesic
The Spectrum of Dynamical Systems Arising from Substitutions of Constant Length
Dekking, F. M.1 
1 Laboratoire de Probabilités, E.R.A. 250 du C-N.R.S., Avenue du Général Leclerc, 35031 Rennes Cédex, France
Publications de l'Institut de recherche mathématiques de Rennes, Séminaire de probabilité I, no. 2 (1976), Exposé no. 6, 34 p.

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Minimal flows and dynamical systems arising from substitutions are considered. In the case of substitutions of constant length the trace relation of the flow is calculated and is used to determine the spectrum of the dynamical system. Several methods are indicated to obtain new substitutions from given ones, leading among other things to a description of the behaviour of powers of the shift homeomorphism on the system arising from any substitution.

Classification : 54H20, 28A65
Keywords: Substitution, trace relation, spectrum, induced transformation

Dekking, F. M. 1

1 Laboratoire de Probabilités, E.R.A. 250 du C-N.R.S., Avenue du Général Leclerc, 35031 Rennes Cédex, France 
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Dekking, F. M. The Spectrum of Dynamical Systems Arising from Substitutions of Constant Length. Publications de l'Institut de recherche mathématiques de Rennes, Séminaire de probabilité I, no. 2 (1976), Exposé no. 6, 34 p. http://geodesic.mathdoc.fr/item/PSMIR_1976___2_A6_0/

1. E. Coven and G.A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973), 138 - 153. | Zbl | MR

2. E. Coven and M. Keane, The structure of substitution minimal sets, Trans. Amer. Math. Soc. 162 (1971), 89 - 102. | Zbl | MR

3. M. Dekking, P. Michel and M. Keane, Substitutions, Seminar, Rennes (1977), unpublished manuscript.

4. Robert Ellis and W.H. Gottschalk, Homomorphisms of transformation groups, Trans. Amer. Math . Soc. 94 (1960), 258 - 271. | Zbl | MR

5. W.H. Gottschalk, Substitution minimal sets, Trans. Amer. Math. Soc. 109 (1963), 467 - 491. | Zbl | MR

6. S. Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635 - 641. | Zbl | MR

7. Teturo Kamae, A topological invariant of substitution minimal sets, J. Math. Soc. Japan 24 (1972), 285 - 306. | Zbl | MR

8. Benjamin G.Klein, Homomorphisms of symbolical dynamical systems, Math. Systems Theory 6 (1972), 107 - 122. | Zbl | MR

9. John C. Martin, Substitution minimal flows, Amer. J. Math 93 (1971), 503 - 526. | Zbl | MR

10. John C. Martin, Minimal flows arising from substitutions of nonconstant length, Math. Systems Theory 7 (1973), 73 - 82. | Zbl | MR

11. P. Michel, Stricte ergodicité d'ensembles minimaux de substitutions, C.R.A.S. 278 (1974), 811 - 813. | Zbl | MR

12. P. Michel, Coincidence values and spectra of substitutions, preprint (1977). | Zbl | MR

13. K. Petersen and L. Shapiro, Induced flows, Trans. Amer. Math. Soc. 177 (1973), 375-389. | Zbl | MR

14. B.L. Van Der Waerden, Modern algebra, vol. 1, second edition, Frederick Ungar Publishing Co New York (1949). | Zbl