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Mild mixing property for special flows under piecewise constant functions

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


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