部分双曲测度的几何性质及其在测度刚性中的应用
动力系统
2024-11-06 v2
摘要
我们给出了由 Katz 引入的、关于三维中部分双曲测度与集合的强稳定与不稳定丛的定量不可积性的几何刻画。这是通过使用不变丛的高阶模板实现的。利用 Katz 近期的工作，我们推导了一些结论，包括 -态的测度刚性以及物理测度的存在性。
引用
@article{arxiv.2302.12981,
title = {Geometric properties of partially hyperbolic measures and applications to measure rigidity},
author = {Alex Eskin and Rafael Potrie and Zhiyuan Zhang},
journal= {arXiv preprint arXiv:2302.12981},
year = {2024}
}
备注
52 pages. Substantial revision thanks to input from several colleagues. Added some flowcharts to describe the structure of the proof and included some toy versions to convey the structure of the proof of some points