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

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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. ***