Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-27 DOI:10.1088/1361-6544/ad4aaf

Livio Flaminio and Davide Ravotti

引用次数: 0

Abstract

We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on -covers, thus proving a strong form of Krickeberg mixing. We also prove that the spectral measures around 0 of the Casimir operators on any increasing sequence of finite Abelian covers converge weakly to an absolutely continuous measure.

查看原文本刊更多论文

双曲面的阿贝尔盖：角环流的等分布谱和无限体积混合渐近线

我们考虑了紧凑双曲面的阿贝尔盖。我们建立了-盖上的角循环流的相关性渐近展开，从而证明了克里克伯格混合的强形式。我们还证明了在任何有限阿贝尔盖的递增序列上，卡西米尔算子在 0 附近的谱度量弱收敛于绝对连续度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.