RUI: Research in Dynamical Systems with Singularities

提出的研究计划旨在对具有奇点的非双曲型系统的动力学现象有更深入的了解。主要目的是研究动力学与生成群的生长和结构之间的相互作用，定义参数的数论性质，限制域的拓扑和几何以及诱导的符号动力系统。程序的范围包括区间交换的推广，多边形对偶台球图，分段等距。这个程序是在动力系统，一个活跃的数学领域，其主要目标是研究对象的长期行为下的应用相同的数学原理。除了在其他数学领域的应用外，该计划还将对电气工程，特别是数字滤波器产生影响。数字滤波器是许多无线和语音识别设备中内置的电子元件中常用的算法。

Abstract for DMS - 0103882The proposed research program seeks to gain a deeper understanding ofthe dynamical phenomena of non hyperbolic systems with singularities. The main goal is to investigate the interplay between dynamics and thegrowth and structure of generating groups, the number theoreticproperties of the defining parameters, and the topology and geometry ofrestricting domains and the induced symbolic dynamical systems. The scope of the program includes generalizations of interval exchanges,polygonal dual billiard maps, piecewise isometries.This program is in dynamical systems, an active area of mathematicswhose main objective is to study long term behavior of objects underapplications of the same mathematical principle. Apart from applicationsin other areas of mathematics, the proposed program will haveimplications in Electrical Engineering, in particular in digitalfilters. Digital filters, are algorithms used commonly in electricalcomponents that built in many wireless and voice recognition devices.