PageHeader : Funkcialaj Ekvacioj, 30 (1987) 305-332
Title : Studies on the Painleve Equations IV.
Title : Third Painleve Equation $\mathrm{P}_{III}$
AuthorInfo : By
AuthorInfo : Kazuo OKAMOTO
AuthorInfo : (University of Tokyo, Japan)
section : Introduction
section : ��1. Painleve system
subsection : 1.1. Painleve equation $\mathrm{P}_{III^{\prime}}$
subsection : 1.2. Painleve system $\mathscr{H}_{III^{\prime}}$
subsection : 1.3. Symmetry of the Hamiltonian $\mathscr{H}_{III^{\prime}}$
subsection : 1.4. Auxiliary Hamiltonian function
subsection : 1.5. Painleve system $\mathscr{H}_{III}$
section : ��2. Transformation group of $\mathscr{H}_{III^{\prime}}$
subsection : 2.1. Root system
subsection : 2.2. Weyl group $\mathrm{W}$
subsection : 2.3. Involution of $\mathrm{E}$
subsection : 2.4. Auxiliary functions
subsection : 2.5. Parallel transformation $\ell$
subsection : 2.6. Realization of $s_{0}$ as the the canonical transformation
section : ��3. Toda equation and ��-functions
subsection : 3.1. ��-function
subsection : 3.2. Proof of Proposition 0.1
subsection : 3.3. Painleve transcendental function and ��-function
subsection : 3.4. Toda equation
subsection : 3.5. Proof of Theorem 2
section : ��4. Cylinder function and Painleve transcendental function
subsection : 4.1. Classical solution
subsection : 4.2. Transformation $\ell_{*}^{-1}$ in the degenerate case
subsection : 4.3. Sequence ofthe cylinder functions
section : References