三维同伦于恒等映射的partially双曲微分同胚，第二部分：分支叶状结构
动力系统
2023-11-22 v2 几何拓扑
摘要
我们研究同伦于恒等映射的 维部分双曲微分同胚，重点关注 Burago 和 Ivanov 的中心稳定与中心不稳定\emph{分支}叶状结构的几何与动力学。这扩展了我们关于动态相干情形中出现的真叶状结构的研究（见\emph{三维同伦于恒等映射的partially双曲微分同胚，第一部分：动态相干情形}，arxiv:1908.06227v3）。我们完成了 Seifert 纤维流形上此类微分同胚的分类。在双曲流形中，我们证明此类微分同胚要么动态相干且存在某次幂为离散化 Anosov 流，要么属于称为\emph{双平移}的新潜在类。
引用
@article{arxiv.2008.04871,
title = {Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations},
author = {Thomas Barthelmé and Sergio R. Fenley and Steven Frankel and Rafael Potrie},
journal= {arXiv preprint arXiv:2008.04871},
year = {2023}
}
备注
This is the second part of arxiv:1908.06227v1 that was split in two. This version has a new part 2-specific introduction and some improved explanations in the text. v2: This is the final accepted version. Some improvements in the text thanks to referees reports