# American Institute of Mathematical Sciences

December  2007, 19(4): 691-710. doi: 10.3934/dcds.2007.19.691

## Mild mixing property for special flows under piecewise constant functions

 1 Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland 2 Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ul. Chopina 12/18, 87-100 Toruń, Poland 3 Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Université François Rabelais de Tours, parc de Grandmont, 37200 Tours, France

Received  November 2006 Revised  April 2007 Published  September 2007

We give a condition on a piecewise constant roof function and an irrational rotation by $\alpha$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence we obtain a class of mildly mixing singular flows on the two-torus that arise from quasi-periodic Hamiltonians flows by velocity changes.
Citation: Krzysztof Frączek, M. Lemańczyk, E. Lesigne. Mild mixing property for special flows under piecewise constant functions. Discrete & Continuous Dynamical Systems, 2007, 19 (4) : 691-710. doi: 10.3934/dcds.2007.19.691
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