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arXiv · 1302.3075

Remarks on step cocycles over rotations, centralizers and coboundaries

Jean-Pierre Conze·Jonathan Marco
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Abstract

By using a cocycle generated by the step function $\varphi_{\beta, \gamma} = 1_{[0, \beta]} - 1_{[0, \beta]} (. + \gamma)$ over an irrational rotation $x \to x + \alpha \mod 1$, we present examples which illustrate different aspects of the general theory of cylinder maps. In particular, we construct non ergodic cocycles with ergodic compact quotients, cocycles generating an extension $T_{\alpha, \varphi}$ with a small centralizer. The constructions are related to diophantine properties of $\alpha, \beta, \gamma$.

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Jean-Pierre Conze, Jonathan Marco. 2013-02-13. Remarks on step cocycles over rotations, centralizers and coboundaries. https://arxiv.org/abs/1302.3075

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