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Differentiable Structures on Fractal Like Sets, Determined by Intrinsic Scaling Functions on Dual Cantor Sets

  • Dennis Sullivan
Part of the NATO ASI Series book series (NSSB, volume 176)

Abstract

There is an easy notion of differentiate structure on a topological space. In the case of an embedded Cantor set in the line the differentiate structure records the fine scale geometrical structure. We will discuss two examples from the theory of one dimensional smooth dynamical systems, namely Cantor sets dynamically defined by i) folding maps on the boundary of chaos,and by ii) smooth expanding maps.

Keywords

Scaling Function Scaling FUNCT Ratio Function Difference Quotient Differentiable Structure 
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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References

  1. 1.
    M. Feigenbaum,The universal metric properties of non linear transformations, J. Statis, Phys.19(1978), 25–52; 21(1979), 669–706.MathSciNetADSzbMATHCrossRefGoogle Scholar
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    P. Coullet, J. Tresser, Iterations d’endomorphisms et groupe de renormalisation, C.R. Acad.Sc., Paris 287(1978), 577; Journal de Physique C5(1978) 25.MathSciNetzbMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Dennis Sullivan
    • 1
  1. 1.The Graduate School and University CenterCity University of New YorkNew YorkUSA

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