In the introduction of [this](http://link.springer.com/article/10.1134%2FS1560354710020243) paper the distribution of the poles of solutions to the first Painlevé equation is discussed.


In particular it is said that the poles form a deformed lattice that degenerates along the rays $\arg(x)=2 n \pi/5,n=0, \pm 1, \pm 2$. The proof seems to be in Boutroux's 1913 paper "Recherches sur les transcendentes de M. Painlev´e et l’´etude asymptotique des ´equations
diff´erentielles du seconde ordre".


Since the paper is in French, I have difficulties understanding the proof.


Can I please get an english reference in which the nature of the poles of $P\_I$ is derived? Alternatively, can I get the derivation as an answer?


Thanks!



Distribution of Poles of solutions to the first Painleve equation
People have difficulties with Boutroux asymptotics not only because his French:-)
And the matter is too complicated to be explained in the space allowed for answers in this site.


You may look at the papers of Kruskal and Joshi, MR0948427 
Joshi, Nalini; Kruskal, Martin D.
An asymptotic approach to the connection problem for the first and the second Painlevé equations. 
Phys. Lett. A 130 (1988), no. 3, 129–137. 


And also this MR1160153. Here is a recent survey:
MR2140299 Steinmetz, Norbert Global properties of the Painlevé transcendents: new results and open questions. Ann. Acad. Sci. Fenn. Math. 30 (2005), no. 1, 71–98.


(There is some disagreement on what is really proved and what is not, concerning these Boutroux asymptotics. Many results belong to physicists and their standards of rigor are different).


