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Published in:
2011 | OriginalPaper | Chapter
Julia and Mandelbrot Sets
Authors : Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas
Published in: An Introduction to Complex Analysis
Publisher: Springer US
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In this lecture, we shall discuss the geometric and topological features of the complex plane associated with dynamical systems whose evolution is governed by the iterative scheme
$$z_n {\rm + 1}\,{\rm = }\,f{\rm (}zn{\rm ), }\,z_{0\,} {\rm = }\,p{\rm }\,{\rm where}\,{\rm }f{\rm (}z{\rm )}$$
is a complex valued function and
$$p\, \in \,C.$$
Such systems occur in physical, engineering, medical, and aesthetic problems, especially those exhibiting chaotic behavior.