Asymptotic behaviour of the fourth Painlev\'e transcendents in the space   of initial values
  We study the asymptotic behaviour of solutions of the fourth Pain\-lev\'e equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalisation of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any non-special solution has an infinite number of poles and infinite number of zeroes. 
Nalini Joshi and Milena Radnovi\'c
nlin.SI math.CA