Asymptotic behaviour of the third Painlev\'e transcendents in the space of initial values
Exactly Solvable and Integrable Systems
2018-01-24 v1 Classical Analysis and ODEs
Abstract
We study the asymptotic behaviour of the solutions of the generic (-type) third Painlev\'e 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 essential singularity at infinity has an infinite number of poles and zeroes, and similarly at the origin.
Keywords
Cite
@article{arxiv.1801.07596,
title = {Asymptotic behaviour of the third Painlev\'e transcendents in the space of initial values},
author = {Nalini Joshi and Milena Radnovic},
journal= {arXiv preprint arXiv:1801.07596},
year = {2018}
}
Comments
36 pages, 6 figures. arXiv admin note: text overlap with arXiv:1703.00100, arXiv:1412.3541