Symmetric Hamiltonian of the Garnier system and its degenerate systems in two variables
arXiv:0706.0799
Abstract
We present {\it symmetric Hamiltonians} for the degenerate Garnier systems in two variables. For these symmetric Hamiltonians, we make the symmetry and holomorphy conditions, and we also make a generalization of these systems involving symmetry and holomorphy conditions inductively. We also show the confluence process among each system by taking the coupling confluence process of the Painlevé systems.
40 pages, 1 figure