{"title":"Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows","authors":"Livio Flaminio and Davide Ravotti","doi":"10.1088/1361-6544/ad4aaf","DOIUrl":null,"url":null,"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.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"59 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad4aaf","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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