Mathematical Sciences: Complex Analytic Dynamics

数学科学：复杂解析动力学

• 批准号: 8801277
• 负责人: Robert Devaney
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801277&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Analytic; Dynamics

Bob Devaney will continue his exciting work on planar dynamical systems. This is part of a program to extend the understanding of rational maps to more general maps in the complex plane. He will continue to study the Julia sets of selected one-parameter families of mappings. These form theboundaries between points with unbounded iterates and those which remain in some fixed region. His innovative use of movies in these studies has been very instructive in our understanding of the dynamics of entire functions, and now seems likely to bear fruit in his investigations of non-analytic dynamics. Devaney will also turn his attention to the bifurcation diagrams of these families. In the realm of analytic dynamics Devaney will work to understand the local dynamics of entire maps near an essential singularity. This is important since one of the distinguishing features of entire functions is the presence of an essential singularity at infinity. In order to extend earlier work to the non-analytic setting he will study non-rational meromorphic functions. There appear to be new dynamical phenomena displayed by the Julia sets of these functions. A final topic for investigation will be the bifurcation structure of the area preserving Henon maps.

鲍勃Devaney将继续他令人兴奋的工作平面动力系统。这是一个程序的一部分，以扩大理解合理的地图，以更一般的地图在复杂的平面。他将继续研究朱莉娅集选定的单参数家庭的映射。这些形式的边界点之间的无限迭代和那些保持在一些固定的区域。他在这些研究中对电影的创新使用，对我们理解整个函数的动力学非常有启发性，现在看来，他对非分析动力学的研究可能会结出果实。Devaney还将把他的注意力转向这些家庭的分叉图。在分析动力学领域，德瓦尼将致力于了解整个地图附近的基本奇点的局部动力学。这一点很重要，因为整函数的一个显著特征是在无穷远处存在本质奇点。为了扩大早期的工作，以非分析设置，他将研究非理性亚纯函数。这些函数的Julia集显示出新的动力学现象。调查的最后一个主题将是分支结构的面积保持Henon地图。