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Sequence Entropy and Mild Mixing

Published online by Cambridge University Press:  20 November 2018

Qing Zhang
Qing Zhang*
Affiliation:
The Ohio State University, 100 Mathematics Building, 231 West 18th Avenue, Columbus, Ohio 43210-1174, USA
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Entropy characterizations of different spectral and mixing properties of dynamical systems were dealt with by a number of authors (see [5], [6] and [8]).

Given an infinite subset Γ = {tn}of N and a dynamical system (X, β,μ, T) one can define sequence entropy along for any finite Petition ξ, and hΓ(T) —supξ hΓ(T,ξ). In [6] Kushnirenko used sequence entropy to give a characterization of systems with discrete spectrum.

Keywords

28D20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 1 , 01 December 1991 , pp. 215 - 224
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Furstenberg, H., IP-systems in ergodic theory, Contemporary Mathematics, Conference in Modern Analysis andProb. 26(1984), 131–148.Google Scholar
2. Furstenberg, H., Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton, N.J., 1981.Google Scholar
3. Furstenberg, H. and Weiss, B., The finite multipliers of infinite ergodic transformations. In: Structure of attractors in dynamical systems. Lecture Notes in Mathematics 688, Springer-Verlag, New York, 1978. 127–133.Google Scholar
4. Hulse, P., Sequence entropy and subsequence generators, J. London Math. Soc. (2) 26(1982), 441–450.Google Scholar
5. Kirillov, A.A., Dynamical systems, factors and representations of groups, Russian Math. Surveys (5) 22(1967), 63–75.Google Scholar
6. Kushnirenko, A.G., On metric invariants of entropy type, Russian Math. Surveys (5) 22(1967), 53–62.Google Scholar
7. Rokhlin, V.A., Lectures on the entropy theory of measure-preserving transformations, Russian Math. Surveys (5) 22(1967), 1–52.Google Scholar
8. Saleski, A., Sequence entropy and mixing, J. Math. Anal. Appl. 60(1977), 58–66.Google Scholar
9. Walters, P., An introduction to ergodic theory. Springer-Verlag, New York, 1982.Google Scholar