当前位置: X-MOL 学术Math. Z. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve
Mathematische Zeitschrift ( IF 0.8 ) Pub Date : 2021-01-07 , DOI: 10.1007/s00209-020-02681-8
Andrey Gogolev , Federico Rodriguez Hertz

In this paper we use the blow-up surgery introduced in [1] to produce new higher dimensional partially hyperbolic flows. The main contribution of the paper is the slow-down construction which accompanies the blow-up construction. This new ingredient allows to dispose of a rather strong domination assumption which was crucial for results in [1]. Consequently we gain more flexibility which allows to construct new volume-preserving partially hyperbolic flows as well as new examples which are not fiberwise Anosov. The latter are produced by starting with the geodesic flow on complex hyperbolic manifold which admits a totally geodesic complex curve. Then by performing the slow-down first and the blow-up second we obtain a new (volume-preserving) partially hyperbolic flows.



中文翻译:

部分双曲动力系统的手术II。复杂曲线的爆破

在本文中,我们使用[1]中介绍的爆炸手术来产生新的高维部分双曲流。本文的主要贡献是伴随爆破施工减速施工。这种新成分可以消除相当强的支配假设,这对于[1]中的结果至关重要。因此,我们获得了更大的灵活性,可以构建新的保留容量部分双曲流以及非纤维状Anosov的新示例。后者是通过在允许完全测地的复曲线的复双曲流形上的测地流开始而产生的。然后,通过先执行减速,然后执行爆破,我们获得了一个新的(保留体积的)部分双曲流。

更新日期:2021-01-08
down
wechat
bug