Etude du formalisme multifractal pour les fonctions
Thesis
نوع عمل المنشور:
دكتوراه.
مدينة النشر:
PARIS FRANCE
رابط المنشور على الويب:
المدرسة:
'ÉCOLE NATIONALE DES PONTS ET CHAUSSÉES
مستخلص المنشور:
Summary The aim of this thesis is the multifractai analysis of selfsimilar functions and the study of the validity of the multifractai formalism. First, we determine the exact pointwise Holder regularity for functions such that locally the graph is roughly a contraction of the global graph, modulo an error; then we compute the Hausdorff dimensions of the sets of points which have the same Holder exponent; and finally we verify the conjectures of Frish and Parisi and the one of Arneodo, Bacry and Muzy, which relate these dimensions to some averaged quantities extracted from the function. We study different types of selfsimilarities, and prove (by reformuling some times) that the wavelet analysis is a good tool to study the validity of these relations.