{"title":"哈密顿动力系统中所有李雅普诺夫指数的正确计算","authors":"D. D. Carpintero, J. C. Muzzio","doi":"10.22201/ia.01851101p.2023.59.02.02","DOIUrl":null,"url":null,"abstract":"The Lyapunov characteristic exponents are a useful indicator of chaos in astronomical dynamical systems. They are usually computed through a standard, very effcient and neat algorithm published in 1980. However, for Hamiltonian systems the expected result of pairs of opposite exponents is not always obtained with enough precision. We find here why in these cases the initial order of the deviation vectors matters, and how to sort them in order to obtain a correct result.","PeriodicalId":49602,"journal":{"name":"Revista Mexicana de Astronomia y Astrofisica","volume":"68 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON THE CORRECT COMPUTATION OF ALL LYAPUNOV EXPONENTS IN HAMILTONIAN DYNAMICAL SYSTEMS\",\"authors\":\"D. D. Carpintero, J. C. Muzzio\",\"doi\":\"10.22201/ia.01851101p.2023.59.02.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Lyapunov characteristic exponents are a useful indicator of chaos in astronomical dynamical systems. They are usually computed through a standard, very effcient and neat algorithm published in 1980. However, for Hamiltonian systems the expected result of pairs of opposite exponents is not always obtained with enough precision. We find here why in these cases the initial order of the deviation vectors matters, and how to sort them in order to obtain a correct result.\",\"PeriodicalId\":49602,\"journal\":{\"name\":\"Revista Mexicana de Astronomia y Astrofisica\",\"volume\":\"68 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Mexicana de Astronomia y Astrofisica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22201/ia.01851101p.2023.59.02.02\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Mexicana de Astronomia y Astrofisica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22201/ia.01851101p.2023.59.02.02","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
ON THE CORRECT COMPUTATION OF ALL LYAPUNOV EXPONENTS IN HAMILTONIAN DYNAMICAL SYSTEMS
The Lyapunov characteristic exponents are a useful indicator of chaos in astronomical dynamical systems. They are usually computed through a standard, very effcient and neat algorithm published in 1980. However, for Hamiltonian systems the expected result of pairs of opposite exponents is not always obtained with enough precision. We find here why in these cases the initial order of the deviation vectors matters, and how to sort them in order to obtain a correct result.
期刊介绍：
The Revista Mexicana de Astronomía y Astrofísica, founded in 1974, publishes original research papers in all branches of astronomy, astrophysics and closely related fields. Two numbers per year are issued and are distributed free of charge to all institutions engaged in the fields covered by the RMxAA.
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