Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech, Edson Denis Leonel
{"title":"An investigation of escape and scaling properties of a billiard system.","authors":"Matheus Rolim Sales, Daniel Borin, Diogo Ricardo da Costa, José Danilo Szezech, Edson Denis Leonel","doi":"10.1063/5.0222215","DOIUrl":null,"url":null,"abstract":"<p><p>We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice that the survival probability follows an exponential decay with a characteristic power-law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find that the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"34 11","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0222215","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice that the survival probability follows an exponential decay with a characteristic power-law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find that the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.
期刊介绍:
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.