Mild mixing property for special flows under piecewise constant functions

Pages: 691 - 710, Volume 19, Issue 4, December 2007

doi:10.3934/dcds.2007.19.691       Abstract        Full Text (371.8K)       Related Articles

Krzysztof Frączek - Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland (email)
M. Lemańczyk - Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Ul. Chopina 12/18, 87-100 Toruń, Poland (email)
E. Lesigne - Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et Techniques, Université François Rabelais de Tours, parc de Grandmont, 37200 Tours, France (email)

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.

Keywords:  Mild mixing property, measure-preserving flows, special flows.
Mathematics Subject Classification:  Primary: 37A10, 37C40; Secondary: 37E35.

Received: November 2006;      Revised: April 2007;      Published: September 2007.