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Mandelbrot and Julia Sets

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Chaos

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Abstract

As already pointed out in Chap. 9, discrete iterated maps appear almost routinely in studies of nonlinear dynamical systems, e.g. as Poincaré maps. Because they are discrete, such maps are much simpler to study (both numerically and analytically) than continuous differential equations. In general, the maps can be written as

$$ {r_{n + 1}} = F({r_n},c) $$
((11.1))

where r = (r 1,..., r N ) is the state vector of the system — for example, a vector in N-dimensional phase space — and c = (r 1,..., r M ) denotes a number of M parameters.

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Authors and Affiliations

  1. Fachbereich Physik, Universität Kaiserslautern, Erwin-Schrödinger-Strasse, D-67663, Kaiserslautern, Germany

    Professor Dr. H. J. Korsch & Professor Dr. H.-J. Jodl

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  1. Professor Dr. H. J. Korsch
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  2. Professor Dr. H.-J. Jodl
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© 1999 Springer-Verlag Berlin Heidelberg

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Korsch, H.J., Jodl, HJ. (1999). Mandelbrot and Julia Sets. In: Chaos. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03866-6_11

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  • DOI: https://doi.org/10.1007/978-3-662-03866-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03868-0

  • Online ISBN: 978-3-662-03866-6

  • eBook Packages: Springer Book Archive

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