Description of Generalized Isomonodromic Deformations of Rank-Two Linear Differential Equations Using Apparent Singularities

In this paper, we consider the generalized isomonodromic deformations of rank-two irregular connections on the Riemann sphere. We introduce Darboux coordinates on the parameter space of a family of rank-two irregular connections by apparent singularities. Using the Darboux coordinates, we describe the generalized isomonodromic deformations as Hamiltonian systems.