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This book—an outgrowth of an international conference held in honor of Jacques Peyrière—provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields. The chapters are thematically organized into five major sections: • Geometric Measure Theory and Multifractals; • Harmonic and Functional Analysis and Signal Processing; • Dynamical Systems and Analysis on Fractals; • Stochastic Processes and Random Fractals; • Combinatorics on Words. Recent Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research. Contributors: J.-P. Allouche, A.M. Atto, J.-M. Aubry, F. Axel, A. Ayache, C. Bandt, F. Bastin, P.R. Bertrand, A. Bonami, G. Bourdaud, Z. Buczolich, M. Clausel, Y. Demichel, X.-H. Dong, A. Durand, A.H. Fan, U.R. Freiberg, S. Jaffard, E. Järvenpää, A. Käenmäki, A. Karoui, H. Kempka, T. Langlet, K.-S. Lau, B. Li, M.M. France, S. Nicolay, E. Olivier, D. Pastor, H. Rao, S.Gy. Révész, J. Schmeling, A. Sebbar, P. Shmerkin, E.C. Waymire, Z.-X. Wen, Z.-Y. Wen, S.C. Williams, S. Winter.

Astronomy -- Mathematics. --- Dimension theory (Topology). --- Fractals. --- Mathematics in nature. --- Fractals --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Mathematics. --- Harmonic analysis. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Functions of complex variables. --- Geometry. --- Probabilities. --- Dynamical Systems and Ergodic Theory. --- Functions of a Complex Variable. --- Probability Theory and Stochastic Processes. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Dimension theory (Topology) --- Differentiable dynamical systems. --- Distribution (Probability theory. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Euclid's Elements --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Complex variables --- Elliptic functions --- Functions of real variables --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics