Global Asymptotics of the Sixth Painlevé Equation in Okamoto’s Space

Abstract

We study dynamics of solutions in the initial value space of the sixth Painlevé equation as the independent variable approaches zero. Our main results describe the repeller set, show that the number of poles and zeroes of general solutions is unbounded and that the complex limit set of each solution exists and is compact and connected.

Keywords

• 34M55
• 34E05
• 34M30
• 14E15