{"title":"一个分岔图能包含环路吗?","authors":"G. Palshin, P. Ryabov, S. Sokolov","doi":"10.1109/NIR52917.2021.9666072","DOIUrl":null,"url":null,"abstract":"The bifurcation diagram plays a major role in the study of the phase topology of completely Liouville-integrable Hamiltonian systems. In the works of A.T. Fomenko and A.V. Bolsinov, the problem of the permissible form of bifurcation diagrams is formulated. In particular, can a bifurcation diagram contain loops? The answer is positive. In this paper, the critical set of the integral mapping and the bifurcation diagram, which contains or almost contains a loop, is given by the example of the vortex dynamics problem.","PeriodicalId":333109,"journal":{"name":"2021 International Conference \"Nonlinearity, Information and Robotics\" (NIR)","volume":"150 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Can a bifurcation diagram contain loops?\",\"authors\":\"G. Palshin, P. Ryabov, S. Sokolov\",\"doi\":\"10.1109/NIR52917.2021.9666072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The bifurcation diagram plays a major role in the study of the phase topology of completely Liouville-integrable Hamiltonian systems. In the works of A.T. Fomenko and A.V. Bolsinov, the problem of the permissible form of bifurcation diagrams is formulated. In particular, can a bifurcation diagram contain loops? The answer is positive. In this paper, the critical set of the integral mapping and the bifurcation diagram, which contains or almost contains a loop, is given by the example of the vortex dynamics problem.\",\"PeriodicalId\":333109,\"journal\":{\"name\":\"2021 International Conference \\\"Nonlinearity, Information and Robotics\\\" (NIR)\",\"volume\":\"150 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 International Conference \\\"Nonlinearity, Information and Robotics\\\" (NIR)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NIR52917.2021.9666072\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 International Conference \"Nonlinearity, Information and Robotics\" (NIR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NIR52917.2021.9666072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The bifurcation diagram plays a major role in the study of the phase topology of completely Liouville-integrable Hamiltonian systems. In the works of A.T. Fomenko and A.V. Bolsinov, the problem of the permissible form of bifurcation diagrams is formulated. In particular, can a bifurcation diagram contain loops? The answer is positive. In this paper, the critical set of the integral mapping and the bifurcation diagram, which contains or almost contains a loop, is given by the example of the vortex dynamics problem.
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