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


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.


Neural Network Statistical Physic Complex System Parameter Space Nonlinear Dynamics 
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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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