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Julia and Mandelbrot Sets

  • Ravi P. Agarwal
  • Kanishka Perera
  • Sandra Pinelas
Chapter

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Kanishka Perera
    • 2
  • Sandra Pinelas
    • 3
  1. 1.Department of MathematicsFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  3. 3.Department of MathematicsAzores UniversityPonta DelgadaPortugal

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