Study of the dynamics of a meromorphic perturbation of the sine family

Abstract

"In this thesis we investigate a family of transcendental meromorphic functionswith one not omitted pole and two parameters. We study the behavior of the familyunder certain assumptions on the parameters and the pole. A definition of a slice ofthe parameter space is given and some examples of approximations of the Fatou andJulia sets are shown. Moreover, some results related with the residual Julia set fortranscendental meromorphic functions are given when the Fatou set has ap−cycle ofHerman rings."