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arXiv · 1506.00444

The Third, Fifth and Sixth Painlev\'e Equations on Weighted Projective Spaces

Hayato Chiba
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Abstract

The third, fifth and sixth Painlev\'e equations are studied by means of the weighted projective spaces ${\mathbb C}P^3(p,q,r,s)$ 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 ${\mathbb C}P^3(p,q,r,s)$ and dynamical systems theory.

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Hayato Chiba. 2015-06-01. The Third, Fifth and Sixth Painlev\'e Equations on Weighted Projective Spaces. https://doi.org/10.3842/sigma.2016.019

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