On some Hamiltonian properties of the isomonodromic tau functions

Alexander Its
Indiana University Purdue University, Indianapolis
Friday, May 11, 2018 - 14:00

We will discuss  some new aspects of the theory of the Jimbo-Miwa-Ueno tau function which  have come to light within the recent developments in the global asymptotic analysis of the  tau functions related to the Painlev\'e equations. Specifically, we will  show that up to the total differentials the logarithmic derivatives of the Painlev\'e tau functions coincide with the  corresponding classical action differential. This fact simplifies considerably the evaluation of the constant factors in the  asymptotics of tau-functions, which has been a long-standing problem of the asymptotic theory of Painlev\'e equations.  The talk is based on the  joint work with A. Prokhorov.

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