### Abstract

In this paper, we study the Painlevé VI equation with parameter (98,−18, 18, 38). We prove (i) An explicit formula to count the number of poles of an algebraic solution with the monodromy group of the associated linear ODE being D_{N}, where D_{N} is the dihedral group of order 2N. (ii) There are only four solutions without poles in C∖{0,1}. (iii) If the monodromy group of the associated linear ODE of a solution λ(t) is unitary, then λ(t) has no poles in R∖{0,1}.

Original language | English |
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Pages (from-to) | 52-63 |

Number of pages | 12 |

Journal | Journal of Geometry and Physics |

Volume | 116 |

DOIs | |

Publication status | Published - 2017 Jun 1 |

Externally published | Yes |

### Keywords

- Algebraic solution
- Painlevé VI equation
- Pole distribution

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

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## Cite this

Chen, Z., Kuo, T. J., & Lin, C. S. (2017). Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I.

*Journal of Geometry and Physics*,*116*, 52-63. https://doi.org/10.1016/j.geomphys.2017.01.016