{"title":"保守地图动态的不确定性","authors":"O. Junge, J. Marsden, I. Mezić","doi":"10.1109/CDC.2004.1430379","DOIUrl":null,"url":null,"abstract":"This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.","PeriodicalId":254457,"journal":{"name":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":"{\"title\":\"Uncertainty in the dynamics of conservative maps\",\"authors\":\"O. Junge, J. Marsden, I. Mezić\",\"doi\":\"10.1109/CDC.2004.1430379\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.\",\"PeriodicalId\":254457,\"journal\":{\"name\":\"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2004.1430379\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2004.1430379","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper studies the effect of uncertainty, using random perturbations, on area preserving maps of R/sub 2/ to itself. We focus on the standard map and a discrete Duffing oscillator as specific examples. We relate the level of uncertainty to the large-scale features in the dynamics in a precise way. We also study the effect of such perturbations on bifurcations in such maps. The main tools used for these investigations are a study of the eigenfunction and eigenvalue structure of the associated Perron-Frobenius operator along with set oriented methods for the numerical computations.
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