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

动力系统研究（数学科学）：女性客座教授

• 批准号: 9102717
• 负责人: Lisa Goldberg
• 金额: $ 7.63万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1993-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102717&HistoricalAwards=false
• 关键词: Research; Dynamical; Systems; Mathematical; Sciences

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.

该项目提出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中的多项式。 它们是之前开始的分析的延伸，根据多项式动态系统在固定点附近的局部行为对多项式动态系统进行分类。 第二组问题涉及 2 圆环和 2 圆盘上的动力系统。 圆环上同一同构的 Denjoy 型定理将被制定。 将在圆盘上概述一种计算机化方法，用于搜索每个圆盘同胚的每个周期循环都与固定点紧密相关的猜想的反例。 研究者正在一个非常活跃的数学领域——动力学的最前沿工作。 该项目进一步推进了 VPW 计划的目标，即为女性提供通过研究促进其在科学或工程领域职业发展的机会，并通过提高研究人员作为所在校园榜样的知名度来鼓励其他女性在这些领域追求职业生涯。 在该项目中，拟议的有助于实现第二个目标的活动包括： 教授一门名为“一维动力学计算机实验”的研究生课程； 每月为对数学研究职业感兴趣的女研究生和高年级本科生举办两次研讨会，包括外部和内部演讲、讨论和咨询。