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.
|Journal||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|Publication status||Published - 2016 Feb 23|
- Painlevé equations
- Weighted projective space
ASJC Scopus subject areas
- Mathematical Physics
- Geometry and Topology