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A sufficient condition for weak mixing of subtitutions and stationary adic transformations. (English. Russian original) Zbl 0713.28011

Math. Notes 44, No. 6, 920-925 (1988); translation from Mat. Zametki 44, No. 6, 785-793 (1988).
See the review in Zbl 0668.28005.

MSC:

28D05 Measure-preserving transformations

Citations:

Zbl 0668.28005
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Full Text: DOI

References:

[1] A. M. Vershik, ?Uniform algebraic approximation of shift and multiplication operators,? Dokl. Akad. Nauk SSSR,259, No. 3, 526-529 (1981). · Zbl 0484.47005
[2] A. M. Vershik, ?Theorem on periodic Markov approximation to ergodic theory,? J. Sov. Math.,28, No. 5 (1985). · Zbl 0559.47006
[3] A. N. Livshits, ?Spectral adic transformations of Markov compacts,? Usp. Mat. Nauk,42, No. 3, 189-190 (1987). · Zbl 0635.47007
[4] F. M. Dekking and M. Keane, ?Mixing properties of substitutions,? Z. Wahrshein. Verw. Geb.,42, 23-33 (1978). · Zbl 0352.28007
[5] P. Michel, ?Coincidence values and spectra of substitutions,? Z. Wahrshein. Verw. Geb.,42, 205-227 (1978). · Zbl 0357.54030
[6] T. Kamae, ?A topological invariant of substitution minimal sets,? Math. Soc. Jpn.,24, No. 2, 285-306 (1972). · Zbl 0232.54052
[7] F. R. Gantmakher, Matrix Theory [in Russian], Nauka, Moscow (1967).
[8] W. H. Gottschalk, ?Substitution minimal sets,? Trans. Am. Math. Soc.,109, 467-491 (1963). · Zbl 0121.18002
[9] J. C. Martin, ?Substitution minimal flows,? Am. J. Math.,93, No. 2, 503-526 (1971). · Zbl 0221.54039
[10] J. C. Martin, ?Minimal flows arising from substitutions of nonconstant length,? Math. Syst. Theor.,7, No. 1, 73-82 (1973). · Zbl 0256.54026
[11] J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, New York (1957). · Zbl 0077.04801
[12] B. Host, ?Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable,? Ergod. Th. Dynam. Sys.,6, 529-540 (1986). · Zbl 0625.28011
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