{"title":"Relativistic effects in the dynamics of a particle in a Coulomb field","authors":"Rafael Ortega , David Rojas","doi":"10.1016/j.physd.2025.134534","DOIUrl":null,"url":null,"abstract":"<div><div>We prove that Bertrand’s property cannot occur in a special-relativistic scenario using the properties of the period function of planar centers. We also explore some integrability properties of the relativistic Coulomb problem and the asymptotic behavior of collision solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134534"},"PeriodicalIF":2.9000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278925000132","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that Bertrand’s property cannot occur in a special-relativistic scenario using the properties of the period function of planar centers. We also explore some integrability properties of the relativistic Coulomb problem and the asymptotic behavior of collision solutions.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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