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This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further 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.

Fractals. --- Fractals --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Mathematics. --- Harmonic analysis. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Partial differential equations. --- Geometry. --- Probabilities. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Partial Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Probability Theory and Stochastic Processes. --- Dimension theory (Topology) --- Differential equations, partial. --- Differentiable dynamical systems. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations --- 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 --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)

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This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further 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.

Mathematics --- Differential geometry. Global analysis --- Geometry --- Functional analysis --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- Partial differential equations --- Differential equations --- Mathematical analysis --- Operational research. Game theory --- Probability theory --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie --- waarschijnlijkheidstheorie --- Fourierreeksen --- stochastische analyse --- functies (wiskunde) --- mathematische modellen --- wiskunde --- wiskunde --- kansrekening --- geometrie --- informatietheorie

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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.

Algebraic geometry --- Geometry --- Functional analysis --- Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory --- Mathematical analysis --- Operational research. Game theory --- Probability theory --- Mathematics --- Classical mechanics. Field theory --- analyse (wiskunde) --- complexe veranderlijken --- waarschijnlijkheidstheorie --- Fourierreeksen --- stochastische analyse --- functies (wiskunde) --- mathematische modellen --- wiskunde --- kansrekening --- geometrie --- dynamica --- informatietheorie

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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