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

本项目的研究包括动力系统领域和复杂分析领域的两组问题。第一组问题涉及单个复变量中的多项式。它们是前面开始的分析的扩展，根据多项式动力系统在固定点附近的局部行为对其进行分类。第二组问题涉及2-环面和2-圆盘上的动力系统。将建立与环面上的恒等式同位的Denjoy型同胚定理。对于每个圆盘同胚的每个周期周期都与一个不动点强相关这一结构，给出了一种寻找反例的计算机化方法。这位研究人员正在研究一个非常活跃的数学领域的前沿--动力学。该项目进一步推动了VPW项目的目标，为女性提供通过研究提升她们在科学或工程领域的职业生涯的机会，并通过调查人员作为东道主校园榜样的更高知名度，鼓励其他女性在这些领域追求职业生涯。在该项目中，促进第二个目标的拟议活动包括：教授题为“一维动力学计算机实验”的研究生课程；为对数学研究职业感兴趣的女研究生和高级本科生每月举办两次研讨会，包括内外演讲、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.