{"title":"Stokes Phenomenon and Spectral Locus in a Problem of Singular Perturbation Theory","authors":"A.A. Arzhanov, S.A. Stepin, V.A. Titov, V.V. Fufaev","doi":"10.1134/S1061920824030026","DOIUrl":null,"url":null,"abstract":"<p> The paper deals with the spectral localization in a model problem of singular perturbation theory and the role of the Stokes phenomenon in this context. We study some typical properties of the asymptotic distribution of eigenvalues and, in particular, topologically different types of the spectral configurations in the semiclassical approximation. In this setting the question naturally arises about the corresponding spectral dynamics and the deformation of the actual limit spectral configurations. </p><p> <b> DOI</b> 10.1134/S1061920824030026 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"351 - 378"},"PeriodicalIF":1.7000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824030026","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The paper deals with the spectral localization in a model problem of singular perturbation theory and the role of the Stokes phenomenon in this context. We study some typical properties of the asymptotic distribution of eigenvalues and, in particular, topologically different types of the spectral configurations in the semiclassical approximation. In this setting the question naturally arises about the corresponding spectral dynamics and the deformation of the actual limit spectral configurations.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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