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

Joshi, Nalini; Radnović, Milena

doi:10.1090/tran/7899

Asymptotic behaviour of the third Painlevé transcendents in the space of initial values
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by Nalini Joshi and Milena Radnović PDF

Trans. Amer. Math. Soc. 372 (2019), 6507-6546 Request permission

Abstract:

We study the asymptotic behaviour of the solutions of the generic ($D_6^{(1)}$-type) third Painlevé equation in the space of initial values as the independent variable approaches infinity (or zero) and show that the limit set of each solution is compact and connected. Moreover, we prove that any solution with an essential singularity at infinity has an infinite number of poles and zeros, and a we obtain a similar result at the origin.

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