Abstract
Let T =(Tft)tϵℝ be a special flow built over an IET T :T→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 the so-called switchable Ratner's property which was introduced in Fayad and Kanigowski [On multiple mixing for a class of conservative surface flows. Invent. Math. to appear]. A consequence of this fact is that such flows are mildly mixing (before, they were only known to be weakly mixing [Ulcigrai. Weak mixing for logarithmic flows over interval exchange transformations. J. Mod. Dynam. 3 (2009), 35-49] and not mixing [Ulcigrai. Absence of mixing in areapreserving flows on surfaces. Ann. of Math. (2) 173 (2011), 1743-1778]). Thus, on each compact, connected, orientable surface of genus greater than one there exist flows that are mildly mixing and not mixing.
Original language | English (US) |
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Pages (from-to) | 2512-2537 |
Number of pages | 26 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 36 |
Issue number | 8 |
DOIs | |
State | Published - Dec 1 2016 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics