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The complex quadratic map and its ℳ-set

In: Fractals and Chaos

Author

Listed:
  • Benoit B. Mandelbrot

    (Yale University, Mathematics Department
    IBM T.J. Watson Research Center)

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.

Suggested Citation

  • Benoit B. Mandelbrot, 2004. "The complex quadratic map and its ℳ-set," Springer Books, in: Fractals and Chaos, chapter 0, pages 73-95, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4017-2_5
    DOI: 10.1007/978-1-4757-4017-2_5
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