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arXiv · 1412.3541

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

Nalini Joshi·Milena Radnović
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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.

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Nalini Joshi, Milena Radnović. 2015-11-26. Asymptotic behaviour of the fourth Painlevé transcendents in the space of initial values. https://arxiv.org/abs/1412.3541

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