Four-Dimensional Painlevé-Type Equations Associated with Ramified Linear Equations I: Matrix Painlevé Systems

Abstract

This series of three papers constructs the complete degeneration scheme of four-dimensional Painlevé-type equations which includes the Painlevé-type equations associated with linear systems of ramified type. In the present paper, we consider the degeneration of Painlevé-type equations which we call the matrix Painlevé systems.