Painleve equations, vector fields, and ranks in differential fields

2016/08/16 by James Freitag, Freitag, James
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AG #math.CA #math.LO #msc:03C60 #msc:14H05 #msc:14H70 #msc:34M55

paper · pdf · doi:10.48550/arxiv.1608.04756

7 pages

arxiv created 2016/08/16 · arxiv updated 2016/08/18

Abstract

Model theoretic ranks of solutions to Painleve equations are calculated, and the type of the generic solution of the second Painleve equation is shown to be disintegrated, strengthening a theorem of Nagloo. A question of Hrushovski and Scanlon regarding Lascar rank and Morley rank in differential fields is answered using planar vector fields.

Related

• Algebraic relations between solutions of Painlevé equations
• A unified approach to the Painleve Transcendents
• Painleve Field Theory
• Open Problems for Painlevé Equations
• Isomonodromy and Painlevé Type Equations, Case Studies