| In this paper, by using Ahlfors's covering surface method, the more general quasimeromorphic mappings are studied, the Julia directions, Borel directions , the largest type Borel directions of quasimeromorphic mappings and the iterations of quasipolynomial mappings are discussed. The following results have been obtained:(1) Two precise theorems of Julia direction are proved.(2)The definition of the largest type Borel directions is introduced,and its existence be proved.The necessary and sufficient condition for judging the largest type Borel direction of K-quasimeromorphic mappings are obtained.(3)The relations between Borel direction and the largest type Borel direction have been discussed, as well as one necesssary and sufficient condition of judging Borel direction of quasimeromorphic mapping is proved.(4) The iteration of quasipolynomial mappings are discussed, some theorems about the escaping set, filling Julia set and Julia set are proved.At the same time, the iterations of two permutable quasipolynomial mappings be discussed. |
