Holomorphic Dynamics

全纯动力学

基本信息

批准号：
1800777
负责人：
Liz Vivas
金额：
$ 15.19万
依托单位：
Ohio State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1800777&HistoricalAwards=false
关键词：
Holomorphic Dynamics

项目摘要

Dynamical systems play an important role in all the sciences. They occur as models for predator and prey populations, orbits of planets and weather conditions. Some of the dynamical systems that are easiest to state are obtained by the iteration of a single map, viewed as a function from the real line to the real line, or from the complex plane to the complex plane. More recently researchers in physical sciences have been interested in models given by higher dimensional mappings. In the complex setting one can make use of complex analytic and geometric tools that are not available in the real one.The aim of this project is to describe the dynamics of a complex analytic map from a space of several variables to itself in the presence of a fixed point that is parabolic. The local study of holomorphic maps close to a fixed point is well understood (although not complete) in one complex dynamics. In several dimensions however, the situation becomes much more complicated. The PI will also focus on global dynamics in this setting and investigate the possible behaviors of orbits and their relation with multipliers at fixed points. Finally, the PI will explore applications of summability theory in the context of parabolic maps in several dimensions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

动态系统在所有科学中都起着重要的作用。它们作为捕食者和猎物种群，行星轨道和天气状况的模型。通过单个映射的迭代获得的某些最容易状态的动态系统，被视为从实际线到实际线的函数，或从复杂平面到复杂平面的函数。最近，物理科学研究人员对较高维映射给出的模型感兴趣。在复杂的环境中，人们可以利用实际尚无可用的复杂分析和几何工具。该项目的目的是描述复杂的分析图的动态，从几个变量的空间到本身，一个抛物线的固定点。在一个复杂的动力学中，对靠近固定点的全态图的本地研究充分了解了（尽管不完整）。但是，在几个维度中，情况变得更加复杂。 PI还将重点关注此环境中的全局动态，并研究轨道的可能行为及其与固定点的乘数的关系。最后，PI将在抛物线图的背景下在几个维度上探索可总结理论的应用。该奖项反映了NSF的法定任务，并使用基金会的智力优点和更广泛的审查标准，被认为值得通过评估来获得支持。