测地流均衡态的局部乘积结构及其应用
动力系统
2024-07-24 v2
摘要
设 为高基数大于等于 2 的紧曲面，配以在有限个锥点处角度大于 的平滑度度量。我们考察 上的测地流，证明其在广泛的均衡态类中具有局部乘积结构。基于此，我们建立了这些系统的伯努利性质。我们也为测地流在秩 1 非正曲率流形上类似均衡态类的局部乘积结构进行了证明。
引用
@article{arxiv.2403.17791,
title = {Local product structure for equilibrium states of geodesic flows and applications},
author = {Benjamin Call and David Constantine and Alena Erchenko and Noelle Sawyer and Grace Work},
journal= {arXiv preprint arXiv:2403.17791},
year = {2024}
}
备注
Fixed an issue with Proposition 3.28 in v1. Added an appendix proving local product structure for a wide class of equilibrium states for geodesic flows on rank 1, nonpositively curved manifolds. 51 pages, 5 figures