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

为该项目提出的研究包括两套 动力系统和复分析领域的问题。 第一组问题涉及多项式在一个单一的复杂 变量 它们是早先开始的分析的延伸， 多项式动力系统的局部分类 在固定点附近的行为。 第二组问题 关于2-torus和2-disk上的动力系统。 Denjoy- 类型理论同胚同位素的身份上的 要制定环面。 一种计算机化的方法来搜索一个 反例的conjucture，每一个周期的周期， 每个圆盘同胚都与一个不动点强联结， 在磁盘上列出。 调查员工作在一个非常活跃的 数学场动力学 该项目进一步推动了VPW计划 目标，为妇女提供机会， 通过研究从事科学或工程职业， 鼓励其他妇女在这些领域从事职业， 调查人员作为东道国榜样的能见度提高 校园。 在这个项目中，拟议的活动， 有助于实现第二个目标包括：教研究生 一维动力学计算机实验课程; 并每月为女毕业生举办两次研讨会， 对研究职业感兴趣的高级本科生， 数学，包括外部和内部扬声器，讨论， 辅导

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.