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. By the Darboux coordinates, we describe the generalized isomonodromic deformations as Hamiltonian systems.