Induced automorphisms and simple approximations
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- by Geoffrey R. Goodson PDF
- Proc. Amer. Math. Soc. 54 (1976), 141-145 Request permission
Abstract:
A class of ergodic, measure preserving invertible point transformations, which are said to admit simple approximations is defined below. If $T$ is an automorphism which admits a simple approximation, conditions are given on a set $A$ so that the induced automorphisms ${T^A}$ and ${T_A}$ again admit simple approximations.References
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- R. V. Chacon and T. Schwartzbauer, Commuting point transformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 11 (1969), 277–287. MR 241600, DOI 10.1007/BF00531651
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- Shizuo Kakutani, Examples of ergodic measure preserving transformations which are weakly mixing but not strongly mixing, Recent advances in topological dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Lecture Notes in Math., Vol. 318, Springer, Berlin, 1973, pp. 143–149. MR 0396911 T. Schwartzbauer, Automorphisms that admit of approximations by periodic transformations, Ph.D. Thesis, University of Minnesota, 1968.
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 141-145
- DOI: https://doi.org/10.1090/S0002-9939-1976-0390171-4
- MathSciNet review: 0390171