Completely squashable smooth ergodic cocycles over irrational rotations
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Cocycles over irrational rotations, squashable cocyclesAbstrakt
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.Pobrania
Opublikowane
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 grudzień 2003, T. 22, nr 2, s. 331–344. [udostępniono 3.7.2024].
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