The Painlev6 property for discrete Hamiltonian systems implies the existence of a symplectic manifold which augments the original phase space and on which the flows exist and are analytic for all times. The augmented manifold is constructed by expanding the Hamilton-Jacobi equation. A complete classification of the types of poles allowed in complex time is given for Hamiltonians which separate ...

In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincare disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painleve function of type VI.

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We provide a Lax pair for the surfaces of Voss and Guichard, we show that such particular considered by Gambier are characterized third Painleve function.

A MACSYMA program is presented which determines whether a given single nonlinear ODE or PDE with real polynomial terms fulfills the necessary conditions for having the Painlevd property. The program listing is given, together with a synopsis of the algorithm, a model of the output of the 0 "S program, a list of tested exarples and instructions to use the package. AMS (MOS) Subject Classificatio...