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Limit cycles created by piecewise linear centers

张祥 教授(上海交通大学)
Tuesday, May 19th, 2020, 9:00 AM  腾讯会议 房间号:366 384 257
报告人简介:张祥教授,欧洲科学与艺术院院士,上海交通大学特聘教授(享受国务院特殊津贴,二级教授、博导)。主要从事动力系统的定性、分支和可积理论的研究。所得结果部分解决了长期遗留的困难的公开问题和猜想,所得结果发表在American J. Math. Transactions of Amer. Math. Soc., Communications Math. Phys., J. Functional Analysis, J. Nonlinear Sciences 和 J. Differential Equations等国际一流数学杂志上。多次应邀在欧美举行的动力系统国际会议上做大会特邀报告。目前担任中国数学会奇异摄动专业委员会主任,中国数学会理事,以及国际SCI杂志《Qualitative Theory of Dynamical Systems》和《International J. Bifurcation and Chaos》的Associate编委等。

These last years the interest for studying the piecewise linear differential systems has increased strongly, mainly due to their applications to many physical phenomena. In the study of these differential systems the limit cycles play a main role.
In this talk we introduce our results on limit cycles of discontinuous piecewise linear differential systems in R^2 formed by three linear centers separated by T type discontinuos lines. We prove that such discontinuous piecewise linear differential systems can have at most 3 limit cycles, with 3 realizable. Moreover, the 3 limit cycles are nested and intersect T in three or four points: either 3 three-point limit cycles, or 1 four-point limit cycle and 2 three-point limit cycles.

主持人:刘兴波 教授
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