Dynamics of Entire Functions: The Fractal Sets of Julia and Mandelbrot

There are very few systematic books on the dynamics of entire functions. Unfortunately, reading these books is often difficult for non-specialists since their proofs are not clearly written, and readers struggle to understand the arguments fully. This book is a comprehensive introduction to the iteration theory of entire complex functions. It is intended to introduce the reader to the key topics in the field and to form a basis for further study. In general, the proofs are more detailed; therefore, the book will also help non-specialist mathematicians become acquainted with complex dynamics. In no sense is this manuscript a complete account of the subject. Nevertheless, the book may also be helpful to young researchers in this field before they tackle more specific works. The book deals with three possible aspects: theory, practice, and computer graphics. In Appendix C, we explained the necessary rudiments of MATLAB RGB images to create computer graphics of different sets considered in the book, such as the sets of Julia and Mandelbrot. In this Appendix, a gallery is also included where beautiful and spectacular images are shown. The author has obtained all these images using MATLAB, most of which are revealed here for the first time.

I was chairman of Mathematics in the University of Huelva (Spain). Now I am retired. I am specialist in Functional Analysis with 43 articles published in different journals and also I have directed four PH D thesis. Some articles are the following ones:

• Operators on Banach spacestaking compact sets inside ranges of vector measures, Proc. Amer. Math. Soc.,116(4),1992.
• The injective hull of an operator ideal on locally convex spaces, Manuscripta mathematica 38,1982
• Vector measure Banach spaces containing a complemented copy of C_0, Proc. Amer. Math. Soc 132(10). 2004
• Operators whose adjoints are quasi-p-nuclear, Studia Mathematica 197(3), 2010