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Anomalous Anosov flows revisited
Proceedings of the London Mathematical Society ( IF 1.5 ) Pub Date : 2020-05-01 , DOI: 10.1112/plms.12321
Thomas Barthelmé 1 , Christian Bonatti 2 , Andrey Gogolev 3 , Federico Rodriguez Hertz 4
Affiliation  

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.

中文翻译:

重访异常的阿诺索夫流

本文致力于高维Anosov流,它由两部分组成。在第一部分中,我们研究了仿射环面纤维上的纤维状Anosov流动,该纤维在3维Anosov上流动。我们为这种流提供了一个二分法结果-它们是Anosov微分形的悬浮或稳定和不稳定的分布具有相等的尺寸。在第二部分中,我们给出了一种新的手术类型的Anosov流结构,该结构可产生所有奇数维的非传递性Anosov流。
更新日期:2020-05-01
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