Advanced Search
Article Contents
Article Contents

Singular continuous spectrum and quantitative rates of weak mixing

Abstract Related Papers Cited by
  • We prove that for a dense $G_{\delta}$ of shift-invariant measures on $A^{\ZZ^d}$, all $d$ shifts have purely singular continuous spectrum and give a new proof that in the weak topology of measure preserving $\ZZ^d$ transformations, a dense $G_{\delta}$ is generated by transformations with purely singular continuous spectrum. We also give new examples of smooth unitary cocycles over an irrational rotation which have purely singular continuous spectrum. Quantitative weak mixing properties are related by results of Strichartz and Last to spectral properties of the unitary Koopman operators.
    Mathematics Subject Classification: Primary: 28D05, 28D20, 58F11.


    \begin{equation} \\ \end{equation}
  • 加载中

Article Metrics

HTML views() PDF downloads(155) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint