Abstract:
The paper presents the study of the iterations of rational fractions, that is, the behavior of z_0,z_1=f(z_0 ),…,z_(n+1)=f(z_n ),… We illustrate the conditions needed for this function to behave as its linear part and prove the existence of Siegel and Cremer points. The study extends to a description of Fatou and Julia sets.
Description:
M.S. -- Faculty of Natural and Applied Sciences, Notre Dame University, Louaize, 2015; "Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematics in the Department of Mathematics and Statistics in the Faculty of Natural and Applied Sciences of Notre Dame University."; Includes bibliographical references (leaves 46).
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