Mathematical Sciences: RUI: Linear- Fractional Models and Their Applications

9401206 Bourdon该项目的重点是开放圆盘上全纯函数的交织映射。给定一个全纯映射，可以使用由交织映射和相关映射组成的对来构造一个模型。该项目考虑了原始贴图中的更改如何影响模型的相互交织的组件。特别地，将对给定全纯映射的交织器序列的收敛性质进行计算机研究。理解这些线性-分式模型的进展将提供对复合算子的行为和迭代下全纯自映射的动力学的洞察。该项目涉及算子论和函数论的相互作用。算子论是研究矩阵无限泛化的数学部分。经典函数论为算子理论提供了模型来源。目前的项目涉及对这样的函数理论模型的研究。这项工作的重要性是与迭代图形计算机计算相联系的结果。本科生参与该项目将对科学产生长期的好处。***

9401206 Bourdon The project focuses on intertwining maps for holomorphic functions on the open disc. Given a holomorphic map a model can be constructed using the pair consisting of the intertwining map and the associated map. The project considers how change in the original map affect the intertwining component of the model. In particular, computer investigations will be made of the convergence properties of a sequence of intertwiners for a given holomorphic map. Progress in understanding these linear-fractional models will provide insight into both the behavior of composition operators and the dynamics of holomorphic self-maps under iteration. The project involves the interplay of operator theory and function theory. Operator theory is that part of mathematics that studies the infinite generalization of matrices. Classical function theory provides a source of models for operator theory. The current project involves a study of such function theoretic models. The importance of this work is a consequence of connections with iterative graphic computer computations. Undergraduate student involvement in the project will have a long term benefit for science. ***