### Abstract

The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces CP^{3}(p, q, r, s) with suitable weights (p, q, r, s) determined by the Newton polyhedrons of the equations. Singular normal forms of the equations, symplectic atlases of the spaces of initial conditions, Riccati solutions and Boutroux's coordinates are systematically studied in a unified way with the aid of the orbifold structure of CP^{3}(p, q, r, s) and dynamical systems theory.

Original language | English |
---|---|

Article number | 019 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 12 |

DOIs | |

Publication status | Published - Feb 23 2016 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

**The third, fifth and sixth painlevé equations on weighted projective spaces.** / Chiba, Hayato.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The third, fifth and sixth painlevé equations on weighted projective spaces

AU - Chiba, Hayato

PY - 2016/2/23

Y1 - 2016/2/23

N2 - The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces CP3(p, q, r, s) with suitable weights (p, q, r, s) determined by the Newton polyhedrons of the equations. Singular normal forms of the equations, symplectic atlases of the spaces of initial conditions, Riccati solutions and Boutroux's coordinates are systematically studied in a unified way with the aid of the orbifold structure of CP3(p, q, r, s) and dynamical systems theory.

AB - The third, fifth and sixth Painlevé equations are studied by means of the weighted projective spaces CP3(p, q, r, s) with suitable weights (p, q, r, s) determined by the Newton polyhedrons of the equations. Singular normal forms of the equations, symplectic atlases of the spaces of initial conditions, Riccati solutions and Boutroux's coordinates are systematically studied in a unified way with the aid of the orbifold structure of CP3(p, q, r, s) and dynamical systems theory.

UR - http://www.scopus.com/inward/record.url?scp=84959241297&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959241297&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2016.019

DO - 10.3842/SIGMA.2016.019

M3 - Article

AN - SCOPUS:84959241297

VL - 12

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 019

ER -