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arXiv · 1409.2987

Ratner's property and mild mixing for smooth flows on surfaces

Adam Kanigowski·Joanna Kułaga Przymus
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Abstract

Let $T=(T_t^f)_{t\in \mathbb{R}}$ be a special flow built over an IET $T : T \to T$ of bounded type, under a roof function f with symmetric logarithmic singularities at a subset of discontinuities of T. We show that $T$ satisfies so-called switchable Ratner's property. A consequence of this fact is that such flows are mildly mixing. Thus, on each compact, connected, orientable surface of genus greater than one there exist flows which are mildly mixing and not mixing.

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Adam Kanigowski, Joanna Kułaga Przymus. 2014-09-10. Ratner's property and mild mixing for smooth flows on surfaces. https://arxiv.org/abs/1409.2987

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