Ce livre fait une revue de diverses techniques d'analyse des courbes planes, en vue des applications. Apres une premiere partie sur les ensembles de mesure nulle sur la droite, une seconde traite des courbes "rectifiables" (de longueur finie), et une troisieme, la plus importante, des courbes fractales. Pour cette seconde edition, certain chapitres ont ete entierement refondus et deux chapitres nouveaux ajoutes sur le theme des spectres multifractals. Cet ouvrage est destine aux chercheurs en sciences experimentales, et comporte un minimum de formalisme mathematique afin de le rendre plus...

A mathematician, a real one, one for whom mathematical objects are abstract and exist only in his mind or in some remote Platonic universe, never "sees" a curve. A curve is infinitely narrow and invisible. Yet, we all have "seen" straight lines, circles, parabolas, etc. when many years ago (for some of us) we were taught elementary geometry at school. E. Mach wanted to suppress from physics everything that could not be perceived: physics and metaphysics must not exist together. Many a scientist was deeply influenced by his philosophy. In his book Claude Tricot tells us that a curve has a...

Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random...