The complex quadratic map and its ℳ-set

  • Benoit B. Mandelbrot
Chapter

Abstract

For each complex μ, denote by F(μ) the largest bounded set in the complex plane that is invariant under the action of the map z → f(z) = z2-μ. M 1980n{C3} and M 1982F{FGN}, Chapter 19 {C4} reported various remarkable properties of the M0 set (the set of those values of the complex μ for which F(μ) contains domains) and of the closure ℳ of ℳ0. {P.S. 2003: see Chapter foreword.} The goals of this work are as follows.

Keywords

Universality Class Stable Cycle Stable Limit Cycle Stable Fixed Point Whirlpool Circle 
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

© Benoit B. Mandelbrot 2004

Authors and Affiliations

  • Benoit B. Mandelbrot
    • 1
    • 2
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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