Skew products of dynamical systems-Reference-Cited by-同舟云学术

Skew products of dynamical systems

Published:1972 Issue:0 Volume:166 Page:27-43
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Kin Eijun

Abstract

In 1950-1951, H. Anzai introduced a method of skew products of dynamical systems in connection with isomorphism problems in ergodic theory. There is a problem to give a necessary and sufficient condition under which an ergodic skew product dynamical system has pure point spectrum. For the special case, translations on the torus, he gave a partial answer for this question. However, this problem has been open in the general case. In the present paper, we generalize the notion of skew products proposed by Anzai and give a complete answer for this problem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1972-166-00/S0002-9947-1972-0296252-9/S0002-9947-1972-0296252-9.pdf

Reference20 articles.

1. Ergodic skew product transformations on the torus;Anzai, Hirotada;Osaka Math. J.,1951

2. È. Hopf, Ergodentheorie, Ergebnisse der Math., Band 5, no. 2, Springer-Verlag, Berlin, 1937, Chaps. 1-4. MR 10, 549.

3. Mixing up property of Brownian motion;Anzai, Hirotada;Osaka Math. J.,1950

4. Stable properties of Gaussian flows;Kin, Eijun;Proc. Japan Acad.,1970

5. Random ergodic theorems and Markoff processes with a stable distribution;Kakutani, Shizuo,1951

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