Remarks on the simple connectedness of basins of sinks for iterations of rational maps
The paper discusses development of the theory of value distribution and growth of meromorphic functions, focusing on two basic notions: exceptional values and asymptotic values. Some historical context is given and contemporary achievements are presented. In particular, recent results concerning exceptional functions and asymptotic functions are considered.
On s’intéresse aux solutions méromorphes sur d’un système de deux équations aux différences à coefficients constants et à deux pas récurrents. Lorsqu’on fait varier ce système, les solutions décrivent une certaine algèbre en rapport avec les fonctions elliptiques habituelles et celles de deuxième espèce de Hermite, ainsi que la fonction de Jacobi. Pour un système donné, les solutions trouvées forment sur le corps des fonctions elliptiques un espace vectoriel de dimension finie, en rapport...
This paper concerns the uniqueness of meromorphic functions and shows that there exists a set S ⊂ ℂ of eight elements such that any two nonconstant meromorphic functions f and g in the open complex plane ℂ satisfying and Ē(∞,f) = Ē(∞,g) are identical, which improves a result of H. X. Yi. Also, some other related results are obtained, which generalize the results of G. Frank, E. Mues, M. Reinders, C. C. Yang, H. X. Yi, P. Li, M. L. Fang and H. Guo, and others.
The aim of this paper paper is to study the comparative growth properties of the composition of entire and meromorphic functions and wronskians generated by them improving some earlier results.