力学系与湍流国家重点实验室学术报告5.17( Professor Gennady Leonov St Petersburg State University, Russia)

发布时间: 2010-05-11 10:47:00　　

 SEMINAR              SERIES

     北京大学工学院      力学与空天技术系

 

    湍流与复杂系统国家重点实验室

 

题目：Attractos, limit cycles and homoclinic orbits in low-dimensional quadraticsystems. (16-th Hilbert problem and Lorenz system)

 

报告人 Professor Gennady Leonov

St Petersburg State University, Russia

 

摘要

Necessary and sufficient conditions for the boundedness of solutions of two-dimensional

quadratic systems in a positively invariant half-plane are given. Generalization of Lienard theorem and application to quadratic system are discussed. Quadratic systems with four limit cycles and perturbed second-order and first-order weak focus are considered. Necessary and

sufficient conditions for existence of homoclinic trajectory of zero saddle of Lorenz system are given. Methods of Lorenz attractor localization are considered. Theory of dimension (topological, Hausdorff, fractal, Lyapunov dimensions) is introduced. Formulas of Lyapunov dimension for Henon and Lorenz attractors are given.

 

简历

Professor Gennady A. Leonov received his Ph.D. in mathematical cybernetics from Saint-Petersburg State University in 1971 and Dr. Sci. in 1983, respectively. Currently, he is a Full Professor at the Mathematics and Mechanics Faculty, as Head of the Applied Cybernetics Department and Director of the Research Institute of Mathematics and Mechanics, as well as the Dean of Mathematics and Mechanics Faculty of Sanit.-Petersburg State University. He was a Vice-Rector of Saint-Petersburg State University from 1986 till 1988.

Professor G.A. Leonov was awarded Prize of Saint.-Petersburg State University (1985), State Prize of USSR (1986), and Prize of Technische Universitet Dresden (1990).

Professor G. A. Leonov is a (Corresponding) Member of the Russian Academy of Science, a Member of the Russian National Committee of Theoretical Mechanics, and a Member of the Directorate of Saint.-Petersburg Mathematical Society.

Professor G. A. Leonov authored and co-authored 300 papers and books.

 

 

主持人:  段志生 教授

时间: 5月17日(周一) 上午10:00 -11:30

地点: 北京大学力学楼四楼434大教室

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