The complex quadratic map and its ℳ-set

  • Benoit B. Mandelbrot


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.


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