On Julia Set of the Functions Which Have Parabolic Fixed Points

Abstract

In the present article, functions with parabolic fixed points are examined and Julia sets have been investigated, including rotational symmetry revealing. Collections of functions which have lines and rays as Julia sets, have been adduced. Construction algorithms for Julia sets of some functions and a number of results obtained by analytical investigations which are visualised by means of computer programs, have been described. Comparison of holomorphic dynamics of a collection of functions which have parabolic fixed point, with holomorphic dynamics of a collection of functions which have attracting fixed point, has been conducted.