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Meromorphic Painlevé transcendents at a fixed singularity

Authors

  • Kazuo Kaneko,

    1. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-oiwakecho, Kyoto, 606-8502, Japan. Phone: +81 75 753 7249, Fax: +81 75 753 7276
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  • Yousuke Ohyama

    Corresponding author
    1. Graduate School of Information Science and Technology, Osaka University, 1-1, Machikane-yama-machi, Toyonaka-city, Osaka, 560-0043, Japan
    • Graduate School of Information Science and Technology, Osaka University, 1-1, Machikane-yama-machi, Toyonaka-city, Osaka, 560-0043, Japan. Phone: +81 6 6850 5311, Fax: +81 6 6850 5326
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  • Dedicated to Professor Kazuo Okamoto on his sixtieth birthday

Abstract

We classify solutions of the third Painlevé equation equation image, which are meromorphic around the origin, and determine their linear monodromy. Combined with 4, 5, all of meromorphic solutions of the Painlevé equations around fixed singular points of the Briot-Bouquet type are completely determined. We characterize the linear monodromy of meromorphic solutions for the third, fifth and sixth Painlevé equations.

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