Singular continuous spectrum in ergodic theory

نویسنده

  • Oliver Knill
چکیده

We prove that in the weak topology of measure preserving transformations , a dense G has purely singular continuous spectrum in the orthocomplement of the constant functions. In the uniform topology, a dense G of aperiodic transformations has singular continuous spectrum. We show that a dense G of shift-invariant measures has purely singular continuous spectrum. These results stay true for Z d actions of measure preserving transformations. There exist smooth unitary cocy-cles over an irrational rotation which have purely singular continuous spectrum.

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تاریخ انتشار 1995