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Analysis of a Fractal Boundary: The Graph of the Knopp Function

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  • Mourad Ben Slimane
  • Clothilde Mélot

Abstract

A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S. Jaffard proposes to compute either weak and strong accessibility exponents or local Lp regularity exponents (the so‐called p‐exponent). These exponents describe locally the behavior of the interface. We apply this method to the graph of the Knopp function which is defined for x ∈ [0, 1] as Fx=∑j=0∞2-αjϕ2jx, where 0

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Handle: RePEc:wly:jnlaaa:v:2015:y:2015:i:1:n:587347
DOI: 10.1155/2015/587347
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