Skew products of dynamical systems

Kin, Eijun

doi:10.1090/S0002-9947-1972-0296252-9

Skew products of dynamical systems
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Trans. Amer. Math. Soc. 166 (1972), 27-43 Request permission

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.

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