Julia and Mandelbrot Sets

Ravi P. Agarwal (), Kanishka Perera () and Sandra Pinelas ()
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Ravi P. Agarwal: Florida Institute of Technology, Department of Mathematics
Kanishka Perera: Florida Institute of Technology, Department of Mathematical Sciences
Sandra Pinelas: Azores University, Department of Mathematics

Chapter Lecture 49 in An Introduction to Complex Analysis, 2011, pp 316-320 from Springer

Abstract: Abstract 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.

Keywords: Complex Plane; Unit Circle; Chaotic System; Iterative Scheme; Periodic Point (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0195-7_49

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DOI: 10.1007/978-1-4614-0195-7_49

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