Julia and Mandelbrot Sets

  • Ravi P. Agarwal
  • Kanishka Perera
  • Sandra Pinelas


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.


Complex Plane Unit Circle Chaotic System Iterative Scheme Periodic Point 
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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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