Ratner’s property and mild mixing for smooth flows on surfaces
Ratner’s property and mild mixing for smooth flows on surfaces
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拉特纳特性和温和混合可实现表面平滑流动
DOI：
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发表时间：
2014
影响因子：
0.9
通讯作者：
J. KUŁAGA
中科院分区：
文献类型：
--
作者：
Adam Kanigowski;J. KUŁAGA
Let ${mathcal{T}}=(T_{t}^{f})_{tin mathbb{R}}$ be a special flow built over an IET $T:mathbb{T}
ightarrow mathbb{T}$ of bounded type, under a roof function $f$ with symmetric logarithmic singularities at a subset of discontinuities of $T$ . We show that ${mathcal{T}}$ 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 area-preserving 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.
Let ${mathcal{T}}=(T_{t}^{f})_{tin mathbb{R}}$ be a special flow built over an IET $T:mathbb{T}
ightarrow mathbb{T}$ of bounded type, under a roof function $f$ with symmetric logarithmic singularities at a subset of discontinuities of $T$ . We show that ${mathcal{T}}$ 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 area-preserving 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.
Teichmüller 动力学中的拉格朗日谱通过重整化
影响因子：
2.2
作者：
Hubert P
通讯作者：
Hubert P