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Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets
Izvestiya: Mathematics ( IF 0.8 ) Pub Date : 2020-10-21 , DOI: 10.1070/im8923
V. Z. Grines 1 , E. D. Kurenkov 1
Affiliation  

We consider orientation-preserving ##IMG## [http://ej.iop.org/images/1064-5632/84/5/862/IZV_84_5_862ieqn1.gif] {$A$} -diffeomorphisms of orientable surfaces of genus greater than one with a one-dimensional spaciously situated perfect attractor. We show that the topological classification of restrictions of diffeomorphisms to such basic sets can be reduced to that of pseudo-Anosov homeomorphisms with a distinguished set of saddles. In particular, we prove a result announced by Zhirov and Plykin, which gives a topological classification of the ##IMG## [http://ej.iop.org/images/1064-5632/84/5/862/IZV_84_5_862ieqn1.gif] {$A$} -diffeomorphisms of the surfaces under discussion under the additional assumption that the non-wandering set consists of a one-dimensional spaciously situated attractor and zero-dimensional sources.

中文翻译:

一维宽敞的基本集的2个流形的微分同构

我们认为保留方向的## IMG ## [http://ej.iop.org/images/1064-5632/84/5/862/IZV_84_5_862ieqn1.gif] {$ A $}-属的可定向表面的变态性更大一个拥有一维空间的完美吸引子的人。我们表明,对这种基本集的变态限制的拓扑分类可以简化为具有一组鞍的拟Anosov同胚。特别地,我们证明了Zhirov和Plykin宣布的结果,该结果给出了## IMG ##的拓扑分类[http://ej.iop.org/images/1064-5632/84/5/862/IZV_84_5_862ieqn1。 gif] {$ A $}-讨论中的曲面的亚同构性,是在非游荡集由一维空间吸引子和零维源组成的附加假设下进行的。
更新日期:2020-10-30
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