Department of Mathematics and Statistics, San Diego State University

Seminars on Differential and Difference Equations,

and Dynamical Systems

Connection problems for linear systems of differential equations in the complex domain

Donald A. Lutz, Mathematics and Statistics, SDSU

This talk will concern some new results about the calculation of connection matrices for solutions of differential equations near regular and irregular singularities. For two dimensional systems, the problems are classical ones and the solutions are the well known hypergeometric or confluent hypergeometric functions; the elements of the connection matrices can be explicitly given in terms of elementary and gamma functions. For higher dimensions, there are no known general formulas for calculating connection matrices as explicit functions of the parameters in the system. But for systems having a special structure which has been identified with interesting deformation properties, connection matrices can be expressed in analogous ways to the classical cases and using similar functions. The process of how these results come about will be described.

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