RUI: Research in Dynamical Systems with Singularities

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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.