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Isomonodromic deformation of $ q$-difference equations and confluence


Author: Thomas Dreyfus
Journal: Proc. Amer. Math. Soc. 145 (2017), 1109-1120
MSC (2010): Primary 39A13, 34M56
DOI: https://doi.org/10.1090/proc/13173
Published electronically: November 18, 2016
MathSciNet review: 3589311
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Abstract: We study isomonodromic deformation of Fuchsian linear $ q$-
difference systems. Furthermore, we are looking at the behaviour of the Birkhoff connection matrix when $ q$ goes to $ 1$. We use our results to study the convergence of the Birkhoff connection matrix that appears in the definition of the $ q$-analogue of the sixth Painlevé equation.


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Additional Information

Thomas Dreyfus
Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne, France
Email: dreyfus@math.univ-lyon1.fr

DOI: https://doi.org/10.1090/proc/13173
Keywords: $q$-difference equations, isomonodromic deformation, Painlev\'e equations, confluence.
Received by editor(s): August 18, 2015
Received by editor(s) in revised form: February 26, 2016
Published electronically: November 18, 2016
Additional Notes: The author’s work was supported by the labex CIMI. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under the Grant Agreement No. 648132.
Communicated by: Mourad Ismail
Article copyright: © Copyright 2016 American Mathematical Society