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An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: Recent Developments

A family of solutions of a degenerate Garnier system near a singularity

19th September 2006

Author: Shun Shimomura (Keio University)

Abstract

The two dimensional Garnier system is obtained from isomonodromic deformation of a Fuchsian differential equation with two deformation parameters. Applying successive limiting procedure to it, H. Kimura computed a degeneration scheme consisting of degenerate Garnier systems written in the Hamiltonian form. Among them, we consider a degenerate Garnier system (G) which is a two variable version of the first Painleve equation. We present a three parameter family of asymptotic solutions of (G) near a singular locus.