三维空间中偏斜 Anosov 流与 Reeb-Anosov 流轨道等价
动力系统
2025-10-30 v4 辛几何
摘要
我们证明在三维空间中，ℝ-覆盖且偏斜的 Anosov 流与 Reeb-Anosov 流轨道等价。我们根据两个不变带号测度之间的环绕数，刻画了不变接触形式或具有给定边界的 Birkhoff 截面的存在性。此外，我们证明了 Reeb-Anosov 流具有一个边界分支的开放书分解的存在性。
引用
@article{arxiv.2301.00842,
title = {Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3},
author = {Théo Marty},
journal= {arXiv preprint arXiv:2301.00842},
year = {2025}
}
备注
73 pages, 3 appendices, 8 figures, 1 table. New version: Section 1 and 2 were merged, explanation were added in section 5, many mistakes were corrected, two figures were added