负曲率流形上测地流的半经典 Zeta 函数
动力系统
2016-10-18 v4
摘要
我们考虑 接触 Anosov 流的半经典（或 Gutzwiller-Voros）Zeta 函数。通过分析与该流相关的转移算子的谱，我们证明对于任意 ，其零点包含在虚轴的 -邻域 与区域 的并集中（至多有限个例外），其中 是流的双曲指数。此外，我们表明虚轴邻域内的零点满足 Weyl 律的类比形式。
引用
@article{arxiv.1311.4932,
title = {The semiclassical zeta function for geodesic flows on negatively curved manifolds},
author = {Frédéric Faure and Masato Tsujii},
journal= {arXiv preprint arXiv:1311.4932},
year = {2016}
}
备注
106 pages, 4 figures. We revised the previous version following comments by the anonymous referee. The main changes are A) the index $k$ in the transfer operators $\mathcal{L}^t_{k,\ell}$ is reversed, B) The content of Subsections 8.2 and 8.3 is exchanged, and C) We rewrote the proof of Lemma 9.4, 9.12 and Lemma 10.11 for clarify of the argument around estimates using integration by parts