## Algebraic solutions of the sixth Painleve equation

Lisovyy, Oleg
Tykhyy, Yuriy
##### Description
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 Painleve VI equation up to parameter equivalence.
Comment: 53 pages, many figures
##### Keywords
Mathematics - Classical Analysis and ODEs, High Energy Physics - Theory, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems