Exceptional solutions to the Painlevé VI equation

Alexandre Eremenko; Andrei Gabrielov; Aimo Hinkkanen

doi:10.1063/1.4973440

Exceptional solutions to the Painlevé VI equation

Alexandre Eremenko
, Andrei Gabrielov
, Aimo Hinkkanen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We find all solutions of the Painlevé VI equations with the property that they have no zeros, no poles, no 1-points, and no fixed points.

Original language	English (US)
Article number	58
Journal	Journal of Mathematical Physics
Volume	58
Issue number	1
DOIs	https://doi.org/10.1063/1.4973440
State	Published - Jan 1 2017

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4973440

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title = "Exceptional solutions to the Painlev{\'e} VI equation",

abstract = "We find all solutions of the Painlev{\'e} VI equations with the property that they have no zeros, no poles, no 1-points, and no fixed points.",

author = "Alexandre Eremenko and Andrei Gabrielov and Aimo Hinkkanen",

note = "We thank Chang-Shou Lin who sent us his work2 and communicated solution (2) before Ref. 3 was released, Clifford Earle for showing us an unpublished letter of Carleson with an elementary proof of Theorem A, and the referee for bringing Ref. 1 to our attention. We also thank Oleg Lisovyy, T. N. Venkataramana, and Math Overflow participants6 for illuminating discussions. Supported by NSF Grant Nos. DMS-1361836 and DMS-1161629.",

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Exceptional solutions to the Painlevé VI equation

Abstract

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