Monodromy dependence and connection formulae for isomonodromic tau functions
DUKE MATHEMATICAL JOURNAL(2018)
Abstract
We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results of M. Bertola, generalizing a previous construction by B. Malgrange. We show how this 1-form can be used to solve a long-standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors. We explain how this scheme works for Fuchsian systems and, in particular, calculate the connection constant for the generic Painleve VI tau function. The result proves the conjectural formula for this constant proposed by Iorgov, Lisovyy, and Tykhyy. We also apply the method to non-Fuchsian systems and evaluate constant factors in the asymptotics of the Painleve II tau function.
MoreTranslated text
Key words
monodromy dependence
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined