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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Skew products of dynamical systems

Author: Eijun Kin
Journal: Trans. Amer. Math. Soc. 166 (1972), 27-43
MSC: Primary 28A65; Secondary 60B99
MathSciNet review: 0296252
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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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Keywords: Generalized flow, simple skew product, N-fold skew product, proper value function, Borel cycle, homology, quasigroup, generalized canonical flow, exact sequence, stability
Article copyright: © Copyright 1972 American Mathematical Society