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Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds

  • V. Yu. Novokshenov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 273)

Abstract

We consider a classification of solutions to the first Painlevé  equation with respect to distribution of their poles at infinity. A connection is found between singularities of two-dimensional monodromy data manifold and analytic properties of solutions parametrized by this manifold. It is proved that solutions of Painlevé  I equation have no poles at infinity at a given critical sector of the complex plane iff the related monodromy data belong to the singular submanifold. Such solutions coincide with the class of “truncated” solutions (intégrales tronquée) by classification of P. Boutroux. We derive further classification based on decomposition of singularities of monodromy data manifold.

Keywords

Painlevé equations Tronquée solution Distribution of poles Riemann-hilbert problem Complex manifold singularities Padé approximations Complex wkb method 

Notes

Acknowledgments

This paper was partly supported by the Russian Science Foundation (RSCF grant 17-11-01004).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Mathematics RASUfaRussia

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