Advanced Search
Article Contents
Article Contents

Non topologically weakly mixing interval exchanges

Abstract Related Papers Cited by
  • In this paper, we prove a criterion for the existence of continuous non constant eigenfunctions for interval exchange transformations which are non topologically weakly mixing. We first construct, for any $m>3$, uniquely ergodic interval exchange transformations of Q-rank $2$ with irrational eigenvalues associated to continuous eigenfunctions which are not topologically weakly mixing; this answers a question of Ferenczi and Zamboni [5]. Moreover we construct, for any even integer $m \geq 4$, interval exchange transformations of Q-rank $2$ with both irrational eigenvalues (associated to continuous eigenfunctions) and non trivial rational eigenvalues (associated to piecewise continuous eigenfunctions); these examples can be chosen to be either uniquely ergodic or non minimal.
    Mathematics Subject Classification: Primary: 35C20, 35P20; Secondary: 93D15.


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

Article Metrics

HTML views() PDF downloads(115) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint