95-193 Knill O.

Singular Continuous Spectrum in Ergodic Theory (30K, LaTeX) Apr 11, 95

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 95-193.tex