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Communications in Mathematical Physics

, Volume 101, Issue 2, pp 283–289 | Cite as

Scaling of Mandelbrot sets generated by critical point preperiodicity

  • J. -P. Eckmann
  • H. Epstein
Article

Abstract

Letzfμ(z) be a complex holomorphic function depending holomorphically on the complex parameter μ. If, for μ=0, a critical point off0 falls after a finite number of steps onto an unstable fixed point off0, then, in the parameter space, near 0, an infinity of more and more accurate copies of the Mandelbrot set appears. We compute their scaling properties.

Keywords

Neural Network Statistical Physic Complex System Parameter Space Nonlinear Dynamics 
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

© Springer-Verlag 1985

Authors and Affiliations

  • J. -P. Eckmann
    • 1
  • H. Epstein
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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