Communications in Mathematical Physics

, Volume 258, Issue 3, pp 513–539 | Cite as

Wavelet Analysis of Fractal Boundaries. Part 1: Local Exponents

  • Stéphane JaffardEmail author
  • Clothilde Mélot


Let Open image in new window be a domain of Open image in new window . In Part 1 of this paper, we introduce new tools in order to analyse the local behavior of the boundary of Open image in new window . Classifications based on geometric accessibility conditions are introduced and compared; they are related to analytic criteria based either on local L p regularity of the characteristic function Open image in new window or on its wavelet coefficients. Part 2 deals with the global analysis of the boundary of Open image in new window . We develop methods for determining the dimensions of the sets where the local behaviors previously introduced occur. These methods are based on analogies with the thermodynamic formalism in statistical physics and lead to new classification tools for fractal domains.


Neural Network Statistical Physic Complex System Characteristic Function 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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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques AppliquéesUniversité Paris XIICréteil CedexFrance
  2. 2.LATPCMI, Université de Provence, 39 rue F. Joliot-CurieFrance

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