Double covering of the Painlevé I equation and its singular analysis

2007/04/22 by Sasano, Yusuke
#32S65 #34M45 #34M55 #58F05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0704.2858

Abstract

In this note, we will do analysis of accessible singular points for a polynomial Hamiltonian system obtained by taking a double covering of the Painlevé I equation. We will show that this system passes the Painlevé α-test for all accessible singular points P_i (i=1,2,3). We note its holomorphy condition of the first Painlevé system.

Related

• Painlevé scheme
• Painleve Test and the Resolution of Singularities for Integrable Equations
• The Painlevé Integrability Test
• The Painlevé equivalence problem for a constrained 3D system
• Explicit Construction of First Integrals by Singularity Analysis in Nonlinear Dynamical Systems