Analysis On Fractals
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Analysis On Fractals
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Author : Jun Kigami
language : en
Publisher:
Release Date : 2001
Analysis On Fractals written by Jun Kigami and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Fractals categories.
Recent Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Birkhäuser
Release Date : 2017-08-23
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Fractals In Music
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Author : Charles B. Madden
language : en
Publisher: High Art Press
Release Date : 1999
Fractals In Music written by Charles B. Madden and has been published by High Art Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.
Analysis Probability And Mathematical Physics On Fractals
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Author : Patricia Alonso Ruiz
language : en
Publisher: World Scientific
Release Date : 2020-02-26
Analysis Probability And Mathematical Physics On Fractals written by Patricia Alonso Ruiz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
Geometry And Analysis Of Fractals
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Author : De-Jun Feng
language : en
Publisher: Springer
Release Date : 2014-08-01
Geometry And Analysis Of Fractals written by De-Jun Feng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
Fractal Based Methods In Analysis
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Author : Herb Kunze
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18
Fractal Based Methods In Analysis written by Herb Kunze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-18 with Mathematics categories.
The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo inOntario. The major focus of their research is on fractals and the applications of fractals.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-22
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-24
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-24 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
The Geometry Of Fractals A New Perspective
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-07
The Geometry Of Fractals A New Perspective written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-07 with Science categories.
Embark on a captivating journey into the realm of fractals, where intricate patterns and self-similarity unveil the hidden beauty and complexity of the natural world. This comprehensive guide delves into the mathematical foundations, applications, and cultural significance of fractals, offering a fresh perspective on these fascinating geometric structures. From the delicate branching of snowflakes to the mesmerizing spirals of seashells, fractals are found in abundance in nature, revealing a level of order within apparent chaos. Botanists, geologists, and meteorologists alike have discovered the fractal patterns that govern the growth of plants, the formation of mountains, and the behavior of clouds. This book takes you on an exploration of the history of fractals, tracing their origins from early mathematical investigations to the groundbreaking work of Benoit Mandelbrot, who brought fractals to the forefront of scientific study. Discover the mathematical concepts that underlie fractal geometry, including set theory, topology, and measure theory. Beyond their mathematical elegance, fractals have found practical applications in diverse fields. Computer scientists utilize fractals to generate realistic images and animations, while engineers harness their properties for signal processing and data compression. Fractals have also inspired new forms of art and music, captivating audiences with their intricate patterns and dynamic forms. This book is not just a scientific treatise; it is an invitation to appreciate the beauty and wonder of fractals. Whether you are a mathematician, a scientist, an artist, or simply someone curious about the world around you, you will find something to engage and inspire you within these pages. **Unveil the Secrets of Fractals:** * Explore the mathematical underpinnings of fractal geometry, including set theory, topology, and measure theory. * Delve into the history of fractals, from early investigations to the groundbreaking work of Benoit Mandelbrot. * Discover the diverse applications of fractals in fields such as computer graphics, image processing, and signal processing. * Appreciate the cultural significance of fractals in art, music, and literature. * Gain a deeper understanding of the beauty and complexity of the natural world through the lens of fractals. If you like this book, write a review on google books!
Chaos Fractals And Complexity
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Author : Tassos Bountis
language : en
Publisher: Springer Nature
Release Date : 2023-09-20
Chaos Fractals And Complexity written by Tassos Bountis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-20 with Science categories.
This volume of proceedings contains research results within the framework of the fields of Chaos, Fractals and Complexity, written by experienced professors, young researchers, and applied scientists. It includes reviews of the fields, which are presented in an educational way for the widest possible audience, analytical results, computer simulations and experimental evidence, focusing on mathematical modelling. The papers presented here are selected from lectures given at the 28th Summer School “Dynamical Systems and Complexity”, July 18 – 27, 2022. Topics cover applications of complex systems in Neuroscience, Biology, Photonics, Seismology, Meteorology, and more broadly Physical and Engineering systems. The summer school has a long history, which began at the University of Patras in 1987 and continues with great success to this day. The original main purpose was to introduce young students and researchers of Greece to a new science that emerged several decades ago and continues to grow internationally at an ever increasing rate around the world.