Degeneration scheme of 4-dimensional Painlev\'e-type equations
  Four 4-dimensional Painlev\'e-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlev\'e system. Degenerating these four source equations, we systematically obtained other 4-dimensional Painlev\'e-type equations. If we only consider Painlev\'e-type equations whose associated linear equations are of unramified type, there are 22 types of 4-dimensional Painlev\'e-type equations: 9 of them are partial differential equations, 13 of them are ordinary differential equations. Some well-known equations such as Noumi-Yamada systems are included in this list. They are written as Hamiltonian systems, and their Hamiltonians are neatly written using Hamiltonians of the classical Painlev\'e equations. 
Hiroshi Kawakami, Akane Nakamura, and Hidetaka Sakai
math.CA nlin.SI