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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.

动力系统在所有科学中起着重要的作用。它们作为捕食者和猎物种群、行星轨道和天气条件的模型出现。一些最容易描述的动力系统是通过单个映射的迭代得到的，该映射被视为从真实的直线到真实的直线的函数，或者从复平面到复平面的函数。最近，物理科学的研究人员对由高维映射给出的模型感兴趣。在复杂的设置可以利用复杂的分析和几何的工具，是不可用于在真实的one.This项目的目的是描述一个复杂的解析映射的动力学从一个空间的多个变量的本身存在的一个固定点是抛物。在一个复动力学中，对全纯映射在不动点附近的局部研究已经很好地理解了（尽管还不完全）。然而，在几个方面，情况变得更加复杂。PI还将专注于在此设置中的全局动力学，并研究轨道的可能行为及其与固定点处乘数的关系。最后，PI将探索求和理论在多维抛物映射中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。