发表机构
The Ohio State University; The Pennsylvania State University（俄亥俄州立大学; 宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过自举提升2-捏合接触Anosov流的共轭正则性，引入辛刚性概念，并证明de la Llave例子在Anosov辛同胚空间中具有刚性，从而建立一系列光滑刚性结果。
AI 中文摘要
本文是作者关于高维接触Anosov流刚性研究论文[GRH]的续篇。在撰写前文时，作者并未注意到Hamenstädt[Ham]更早的工作也致力于同一问题。[GRH]与[Ham]的方法有所重叠但不完全相同。本文通过进一步自举2-捏合接触Anosov流共轭的正则性，加强了Hamenstädt的部分结果。我们还引入了辛同胚的辛刚性概念，并证明某些Anosov微分同胚具有辛刚性。我们进一步将辛刚性与其他刚性技术相结合，建立了若干关于Anosov辛同胚的光滑刚性结果。在Anosov辛同胚领域出现了一些新现象。例如，著名的de la Llave在4-环面上的例子表明在光滑Anosov微分同胚空间中缺乏刚性，然而我们证明该例子在Anosov辛同胚空间中却是刚性的。
英文摘要
This paper is a sequel to the authors' paper on rigidity of higher dimensional contact Anosov flows~[GRH]. At the time the authors were unaware of much earlier work of Hamenstädt~[Ham] devoted to the same problem. The methods of~[GRH] and~[Ham] are overlapping but not entirely the same. In this paper we strengthen some the results of Hamenstädt, by further bootstrapping the regularity of the conjugacy of 2-pinched contact Anosov flows. We also introduce a notion of symplecto-rigidity for symplectomorphisms and prove that some Anosov diffeomorphisms are symplecto-rigid. We further combine symplecto-rigidity with various rigidity techniques to establish a number of smooth rigidity results of Anosov symplectomorphisms. Some new phenomena are present in the realm of Anosov symplectomorphism. For example, while the well-known de la Llave example on the 4-torus demonstrates absence of rigidity in the space of smooth Anosov diffeomorphisms, however, we prove that it is rigid in the space of Anosov sympelctomorphisms.
Comments14 pages
