Hamiltonian representation of isomonodromic deformations of general rational connections on $\mathfrak{gl}_2(\mathbb{C})$

In this paper, we construct the Hamiltonian systems attached to generic $\mathfrak{gl}_2(\mathbb{C})$ meromorphic connections with an arbitrary number of unramified poles of arbitrary orders, under the assumption that every leading polar coefficient is regular semisimple. In particular, we propose t