Completely squashable smooth ergodic cocycles over irrational rotations
Keywords
Cocycles over irrational rotations, squashable cocyclesAbstract
Let $\alpha$ be an irrational number and the trasformation $$ Tx \mapsto x+\alpha \bmod 1, \quad x\in [0,1), $$ 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.Downloads
Published
2003-12-01
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1.
VOLNÝ, Dalibor. Completely squashable smooth ergodic cocycles over irrational rotations. Topological Methods in Nonlinear Analysis. Online. 1 December 2003. Vol. 22, no. 2, pp. 331 - 344. [Accessed 19 April 2024].
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