Mild mixing property for special flows under piecewise constant functions

Mathematics – Dynamical Systems

Scientific paper

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Accepted for publication in Discrete Contin. Dyn. Syst

Scientific paper

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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