Constructive Approximation

, Volume 43, Issue 3, pp 337–356 | Cite as

Fixed Points for the Multifractal Spectrum Map

  • Delphine Maman
  • Stéphane SeuretEmail author


For all continuous function g having a specific form that we call with increasing visibility, we construct a function f whose multifractal spectrum is such that \( d_f =g\circ f\). The function f is obtained as an infinite superposition of piecewise \(C^1\) functions, is also with increasing visibility, and is homogeneously multifractal; i.e., its restriction on any subinterval of \([0,1]\) has the same multifractal spectrum as the function f itself. In particular, we prove the existence of a function f which is its own multifractal spectrum; i.e., \(f=d_f\).


Local regularity Hausdorff dimension and measure Multifractals Hölder exponent 

Mathematics Subject Classification

26A16 28A80 28C15 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.LAMA (UMR 8050), UPEMLV, UPEC, CNRSUniversité Paris-EstCréteilFrance

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