Algebraic solutions of the sixth Painlevé equation

Oleg Lisovyy (1) , Yuriy Tykhyy

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We describe all finite orbits of an action of the extended modular group $\bar{\Lambda}$ on conjugacy classes of SL(2,C)-triples. The result is used to classify all algebraic solutions of the general Painlevé VI equation up to parameter equivalence.

Domaines: Analyse classique [math.CA]; Systèmes Solubles et Intégrables [nlin.SI]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Oleg Lisovyy, Yuriy Tykhyy. Algebraic solutions of the sixth Painlevé equation. 2008. ⟨hal-00783927⟩