A class of mixing special flows overtwo--dimensional rotations

Krzysztof Frączek; Mariusz Lemańczyk

doi:10.3934/dcds.2015.35.4823

Article Contents

2015, Volume 35, Issue 10: 4823-4829. Doi: 10.3934/dcds.2015.35.4823

This issue Previous Article Schrödinger equations with rough Hamiltonians Next Article Ergodicity of two particles with attractive interaction

A class of mixing special flows over two--dimensional rotations

Krzysztof Frączek^1, and
Mariusz Lemańczyk^2,

1.
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń
2.
Faculty of Mathematics and Computer Science, N. Copernicus University, ul. Chopina 12/18, 87-100 Toruń

Received: September 30, 2014

Revised: January 31, 2015

Published: September 2015

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Abstract

We consider special flows over two-dimensional rotations by $(\alpha,\beta)$ on $\mathbb{T}^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition \[\int_{\mathbb{T}^2}f_x(x,y)\,dx\,dy\neq 0\quad\text{ and }\quad \int_{\mathbb{T}^2}f_y(x,y)\,dx \,dy\neq 0.\] For an uncountable set of $(\alpha,\beta)$ with both $\alpha$ and $\beta$ of unbounded partial quotients the mixing property is proved to hold.

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Mathematics Subject Classification: 37A10, 37A25.

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References

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