Perturbative methods for the Painlev\'e test
solv-int
2007-05-23 v1 可精确求解与可积系统
摘要
There exist many situations where an ordinary differential equation admits a movable critical singularity which the test of Kowalevski and Gambier fails to detect. Some possible reasons are: existence of negative Fuchs indices, insufficient number of Fuchs indices, multiple family, absence of an algebraic leading order. Mainly giving examples, we present the methods which answer all these questions. They are all based on the theorem of perturbations of Poincar\'e and computerizable.
引用
@article{arxiv.solv-int/9812007,
title = {Perturbative methods for the Painlev\'e test},
author = {R. Conte},
journal= {arXiv preprint arXiv:solv-int/9812007},
year = {2007}
}
备注
11 pages, no figure, standard Latex, to appear in the proceedings of ``Nonlinear dynamics: integrability and chaos'', Tiruchirapalli, 12--16 Feb 1998, ed. S. Daniel