Asymptotic behaviour of the fourth Painlevé transcendents in the space of initial values

2014/12/11 by Nalini Joshi, Joshi, Nalini, Milena Radnović +1
Computer Science · Mathematics · Physics and Astronomy · #34M30 #34M55 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #math.CA #msc:34M30 #msc:34M55 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1412.3541

30 pages, 1 figure; Added Section 3 on the special solutions

openalex publication_date 2014/12/11 · arxiv created 2015/11/26 · arxiv updated 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of solutions of the fourth Pain\-levé equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalisation of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any non-special solution has an infinite number of poles and infinite number of zeroes.

Related

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• Classification of Real Solutions of the Fourth Painleve Equation
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