报告人：Warwick Tucker

报告题目：The Songling system has exactly four limit cycles

时间：2025年11月03日 10:00-11:30

地点：数学楼2-1

报告摘要：

Determining how many limit cycles a planar polynomial system of differential equations can have is a remarkably hard problem. One of the main difficulties is that the limit cycles can reside within areas of vastly different scales. This makes numerical explorations very hard to perform, requiring high precision computations, where the necessary precision is not known in advance. Using rigorous computations, we can dynamically determine the required precision, and localise all limit cycles of a given system. We prove that the Songling system of planar, quadratic polynomial differential equations has exactly four limit cycles. Furthermore, we give precise bounds for the positions of these limit cycles using rigorous computational methods based on interval arithmetic. The techniques presented here are applicable to the much wider class of real-analytic planar differential equations. This is joint work with Zbigniew Galias.

报告人简介：

Professor Warwick Tucker obtained his PhD from Uppsala University in 1998 under the supervision of Lennart Carleson. He has held positions at IMPA, Cornell University, University of Bergen, ENS-Lyon, and Uppsala University, where he served as the Head of Department 2014-2020. Since 2020 Professor Tucker is the Head of School of Mathematics at Monash University. In his research, he focuses on advancing the frontiers of computer-aided proofs in mathematical analysis. In 2004 Professor Tucker was awarded the EMS Prize for distinguished contributions in Mathematics, notably on his work regarding the Lorenz attractor. He is also the author of the book "Validated numerics: a short introduction to rigorous computations".