Mild mixing property for special flows under piecewise constant functions

Krzysztof Frączek; M. Lemańczyk; E. Lesigne

doi:10.3934/dcds.2007.19.691

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2007, Volume 19, Issue 4: 691-710. Doi: 10.3934/dcds.2007.19.691

This issue Previous Article On small amplitude solutions to the generalized Boussinesq equations Next Article A note on a non-local Kuramoto-Sivashinsky equation

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

Received: October 31, 2006

Revised: March 31, 2007

Published: September 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 37A10, 37C40; Secondary: 37E35.

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