TITLE:
Conditions Where the Chaotic Set Has a Non-Empty Residual Julia Set for Two Classes of Meromorphic Functions
AUTHORS:
Patricia Domínguez, Iván Hernández
KEYWORDS:
Fatou Set; Julia Set; Residual Julia Set; Buried Points; Buried Components
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11B,
November
7,
2013
ABSTRACT:
We define the Fatou and Julia sets for two classes of
meromorphic functions. The Julia set is the chaotic set where the fractals
appear. The chaotic set can have points and components which are buried. The
set of these points and components is called the residual Julia set,
denoted by , and is defined to be the subset of those points of the
Julia set, chaotic set, which do not belong to the boundary of any component of
the Fatou set (stable set). The points of are called buried
points and the components of are called buried
components. In this paper we extend some results related with the residual
Julia set of transcendental meromorphic functions to functions which are
meromorphic outside a compact countable set of essential singularities. We give
some conditions where .