ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION
ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION
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关于环面的环形图和次线性扩散
DOI：
10.1017/s1474748016000268
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发表时间：
2013
影响因子：
0.9
通讯作者：
Pablo Dávalos
中科院分区：
文献类型：
--
作者：
Pablo Dávalos
Misiurewicz和Ziemian的一篇经典文章（J. Lond. Math.Soc.40（2）（1989），490-506）根据$\unicode [STIX]{x1 D 70 C}$是点、线段还是具有非空内部的集合，通过旋转集合$\unicode [STIX]{x1 D 70 C}$对Homeo $_{0}（\mathbf{T}^{2}）$中的元素进行分类。最近Koropecki和Tal在（Invent.）中给出了Homeo $_{0}（\mathbf{T}^{2}）$中非游荡元素的分类。196（2014），339-381），根据动力学发生的内在底层环境空间：平面、环形和严格的环面映射。我们研究这两个分类之间的联系，表明，即使在国外的nonwandering设置，环形地图的特点是旋转集是合理的部分。此外，我们得到的信息，次线性扩散的轨道在不太好理解的情况下，$\unicode[STIX]{x1 D 70 C}$有非空的内部。
A classical article by Misiurewicz and Ziemian (J. Lond. Math. Soc. 40(2) (1989), 490–506) classifies the elements in Homeo $_{0}(\mathbf{T}^{2})$ by their rotation set $\unicode[STIX]{x1D70C}$ , according to wether $\unicode[STIX]{x1D70C}$ is a point, a segment or a set with nonempty interior. A recent classification of nonwandering elements in Homeo $_{0}(\mathbf{T}^{2})$ by Koropecki and Tal was given in (Invent. Math. 196 (2014), 339–381), according to the intrinsic underlying ambient space where the dynamics takes place: planar, annular and strictly toral maps. We study the link between these two classifications, showing that, even abroad the nonwandering setting, annular maps are characterized by rotation sets which are rational segments. Also, we obtain information on the sublinear diffusion of orbits in the—not very well understood—case that $\unicode[STIX]{x1D70C}$ has nonempty interior.