FORMAL STABILITY OF ELLIPTIC EQUILIBRIA. APPLICATIONS
报告人：Patricia Yanguas
报告地点：数学与统计学院二楼会议室
报告时间：2023年6月30日 15：30-16：30
邀请人：李勇、冀书关
报告摘要：
The subject of this talk is the study of the nonlinear stability of elliptic equilibria in Hamiltonian systems with n degrees of freedom. We provide a criterion to obtain formal stability. This result generalises previous approaches, such as exponential stability in the sense of Nekhoroshev when there is directional quasi-convexity. It is also applicable to highly degenerate systems. Moreover, in case of formal stability, the solutions are proven to be bounded near the equilibrium over exponentially long times. The theory is illustrated with some applications to systems with three or more degrees of freedom: the spatial circular restricted three body problem; the attitude motion of a satellite describing a circular orbit in space with respect to its centre of mass in a central gravitational field; the Levitron.
主讲人简介：
She is doctor in Mathematics by Universidad Publica de Navarra since 1998. She received the Doctoral Thesis Prize by Universidad Publica de Navarra in Basic Science and Health Science corresponding to the academic years 1996/97 and 1997/98. She obtained a grant from Gobierno de Navarra or a six-months research stay at Leiden University (The Netherlands). In 1996 she joined Universidad Publica de Navarra as part-time Associate Lecturer of Applied Mathematics in the Department of Mathematics and Informatics of the time. In 2000 she became Senior Lecturer in Applied Mathematics. Her research area is Applied Mathematics and, specifically, differential
equations, dynamical systems and celestial mechanics. From 2008 to 2012 she was Deputy Head of the then School of Agricultural Engineering. At present, together with Joan Torregrosa, she is Director of the DANCE (Dynamics, Attractors and Nonlinearity: Chaos and Stability) network.
学校主页