北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > BIMSA Integrable Systems Seminar Andronov School of Nonlinear Oscillations
Andronov School of Nonlinear Oscillations
组织者
尼古拉·莱舍提金 , 伊万·谢钦 , 安德烈·茨加诺夫
演讲者
Olga Pochinka
时间
2023年10月17日 16:00 至 18:00
地点
A6-101
摘要
Andronov's school began to take shape in 1931, when Alexander Alexandrovich himself, together with his wife E.A. Leontovich, moved from Moscow to Nizhny Novgorod. By the time of the move, A.A. Andronov was an established scientist. Even then, he introduced a number of new concepts into science, including self-oscillations, concepts of the roughness of the system, the bifurcation value of the parameter, the phase portrait, and so on. This is a long-lived school in which a unified scientific program has been actively developed by several generations of scientists. In my report, I will touch upon the scientific direction of the school, which is associated with rough (structurally stable) dynamic systems. The simplest of them - "Morse-Smale systems" got their name after the publication of S. Smale's work "On gradient dynamical system // Ann. Math. 74, 1961, P.199-206". He introduced a class of flows on manifolds of arbitrary dimension that copy the properties of coarse flows on the plane described in 1937 by A. Andronov and L. Pontryagin. For the introduced streams Smale proved the validity of inequalities similar to Morse inequalities for non-degenerate functions, after which such flows were called Morse-Smale flows. S. Smale considered it extremely important to study such flows, since he assumed that, by analogy with coarse flows on the plane, Morse-Smale flows exhaust the class of structurally stable flows on manifolds and are dense in the set all threads. Fortunately, it turned out that the multidimensional structurally stable world is much wider, and the Morse-Smale systems represent only its regular part - structurally stable systems with a non-wandering set consisting of a finite number of orbits. Due to the close connection of Morse-Smale systems with the carrier manifold, various topological objects, including wild ones, are realized as invariant subsets of such systems. This leads to a wide variety of Morse-Smale systems (especially on multidimensional manifolds) and, accordingly, complicates their topological classification.
北京雁栖湖应用数学研究院
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