Research in Dynamical Systems (Mathematical Sciences): Visiting Professorships for Women

本项目拟进行的研究包括动力系统和复杂分析领域的两组问题。第一组问题涉及单个复变量的多项式。它们是前面开始的分析的扩展，根据它们在不动点附近的局部行为对多项式动力系统进行分类。第二组问题涉及2环面和2盘上的动力系统。给出了环面上恒等同胚的Denjoy型定理。在磁盘上勾画出一种计算机化的方法，用以寻找一个反例来证明每一个磁盘同胚的每一个周期都与一个不动点紧密相连。研究者在一个非常活跃的数学领域——动力学的前沿工作。该项目进一步推进了VPW项目的目标，即通过研究为女性提供在科学或工程领域发展的机会，并通过研究人员在东道国校园中作为榜样的知名度提高，鼓励其他女性在这些领域追求职业。在这个项目中，提出的有助于第二个目标的活动包括：教授一门名为“一维动力学中的计算机实验”的研究生课程；每月两次为对数学研究事业感兴趣的女研究生和高级本科生举办研讨会，包括外部和内部演讲，讨论和咨询。

The research proposed for this project consists of two sets of questions in the field of dynamical systems and complex analysis. The first set of problems concerns polynomials in a single complex variable. They are an extension of the analysis begun earlier, classifying polynomial dynamic systems in terms of their local behavior near the fixed points. The second set of problems concerns dynamical systems on the 2-torus and the 2-disk. Denjoy- type theorms for homeomorphisms isotopic to the identity on the torus are to be formulated. A computerized method to search for a counterexample to the conjucture that every periodic cycle for every disc homeomorphism is strongly linked with a fixed point is to be outlined on the disk. The investigator is working in the forefront of a very active methematical field--dynamics. The project furthers VPW program objectives to provide opportunities for women to advance their careers in science or engineering through research, and to encourage other women to pursue careers in these areas through the investigators' enhanced visibility as role models on the host campuses. In this project, the proposed activities which contribute to the second objective include: teaching a graduate course entitled Computer Experiments in One-Dimensional Dynamics; and conducting twice-monthly seminars for female graduate and advanced undergraduate students interested in research careers in mathematics, including outside and inside speakers, discussion, and counselling.