Topological Methods in Nonlinear Analysis

Completely squashable smooth ergodic cocycles over irrational rotations

Dalibor Volný

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Abstract

Let $\alpha$ be an irrational number and the trasformation $$ Tx \mapsto x+\alpha\,{\rm mod}\,1, \quad x\in [0,1), $$ represent an irrational rotation of the unit circle. We construct an ergodic and completely squashable smooth real extension, i.e. we find a real analytic or $k$ time continuously differentiable real function $F$ such that for every $\lambda\neq 0$ there exists a commutor $S_\lambda$ of $T$ such that $F\circ S_\lambda$ is $T$-cohomologous to $\lambda\varphi$ and the skew product $T_F(x,y) = (Tx, y+F(x))$ is ergodic.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 22, Number 2 (2003), 331-344.

Dates
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475266340

Mathematical Reviews number (MathSciNet)
MR2036380

Zentralblatt MATH identifier
1057.37003

Citation

Volný, Dalibor. Completely squashable smooth ergodic cocycles over irrational rotations. Topol. Methods Nonlinear Anal. 22 (2003), no. 2, 331--344. https://projecteuclid.org/euclid.tmna/1475266340


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