ASYMPTOTIC BEHAVIOUR OF THE THIRD PAINLEVE TRANSCENDENTS IN THE SPACE OF INITIAL VALUES

摘要

We study the asymptotic behaviour of the solutions of the generic (D-6((1))-type) third Painleve 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.