95-193 Knill O.
Singular Continuous Spectrum in Ergodic Theory (30K, LaTeX) Apr 11, 95
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Abstract. We prove that in the weak topology of measure preserving transformations, a dense $G_{\delta}$ has purely singular continuous spectrum in the orthocomplement of the constant functions. In the uniform topology, a dense $G_{\delta}$ of aperiodic transformations has singular continuous spectrum. We show that a dense $G_{\delta}$ of shift-invariant measures has purely singular continuous spectrum. These results stay true for $\ZZ^d$ actions of measure preserving transformations. There exist smooth unitary cocycles over an irrational rotation which have purely singular continuous spectrum.

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