Painlevé σ-equations s1, s2, s4 and Their Value Distribution


Ewa Ciechanowicza




Local solutions of Painlevé equations P 1 , P 2 , P 4 , as well as of the equations S 1 , S 2 , S 4 satisfied by their Hamiltonians, can be extended to functions meromorphic in C. This way they become a point of interest for value distribution theory. Distribution of values of solutions of P 1 , P 2 and P 4 is already well described. In the paper we discuss mostly S 1 , S 2 and S 4 in this context. In particular, we pay attention to deficient, asymptotic and ramified values of solutions of these equations.