Brownian Motion On Nested Fractals

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Brownian Motion On Nested Fractals

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Author : Tom Lindstrøm
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Brownian Motion On Nested Fractals written by Tom Lindstrøm 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 1990 with Mathematics categories.

Lindstrom (U. of Oslo) constructs Brownian motion on a reasonably general class of self-similar fractals. He deals with diffusions, self-similar fractals, fractal Laplacians, asymptotic distribution of eigenvalues, nonstandard analysis. Annotation copyright Book News, Inc. Portland, Or.

Brownian Motion On Nested Fractals

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Author : Tom Lindstrom
language : it
Publisher:
Release Date : 1990

Brownian Motion On Nested Fractals written by Tom Lindstrom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

Analysis On Fractals

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Author : Jun Kigami
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-07

Analysis On Fractals written by Jun Kigami and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-07 with Mathematics categories.

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.

Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot

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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus 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 2004 with Mathematics categories.

This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

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.

Differential Equations On Fractals

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Author : Robert S. Strichartz
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05

Differential Equations On Fractals written by Robert S. Strichartz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Mathematics categories.

Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals. Written in a lively and informal style, with lots of intriguing exercises on all levels of difficulty, the book is accessible to advanced undergraduates, graduate students, and mathematicians who seek an understanding of analysis on fractals. Robert Strichartz takes the reader to the frontiers of research, starting with carefully motivated examples and constructions. One of the great accomplishments of geometric analysis in the nineteenth and twentieth centuries was the development of the theory of Laplacians on smooth manifolds. But what happens when the underlying space is rough? Fractals provide models of rough spaces that nevertheless have a strong structure, specifically self-similarity. Exploiting this structure, researchers in probability theory in the 1980s were able to prove the existence of Brownian motion, and therefore of a Laplacian, on certain fractals. An explicit analytic construction was provided in 1989 by Jun Kigami. Differential Equations on Fractals explains Kigami's construction, shows why it is natural and important, and unfolds many of the interesting consequences that have recently been discovered. This book can be used as a self-study guide for students interested in fractal analysis, or as a textbook for a special topics course.

Fractal Geometry And Stochastics Ii

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Author : Christoph Bandt
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Fractal Geometry And Stochastics Ii written by Christoph Bandt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The second conference on Fractal Geometry and Stochastics was held at Greifs wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.

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.

Seminar On Stochastic Processes 1992

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Author : Cinlar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Seminar On Stochastic Processes 1992 written by Cinlar 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 2012-12-06 with Mathematics categories.

The 1992 Seminar on Stochastic Processes was held at the Univer sity of Washington from March 26 to March 28, 1992. This was the twelfth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, University of Florida, University of Virginia, University of California, San Diego, University of British Columbia and University of California, Los An geles. Following the successful format of previous years, there were five invited lectures, delivered by R. Adler, R. Banuelos, J. Pitman, S. J. Taylor and R. Williams, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants cre ated a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1992 Seminar was made possible through the support of the National Science Foundation, the National Security Agency, the Institute of Mathematical Statistics and the University of Washing ton. We extend our thanks to them and to the publisher Birkhauser Boston for their support and encouragement. Richard F. Bass Krzysztof Burdzy Seattle, 1992 SUPERPROCESS LOCAL AND INTERSECTION LOCAL TIMES AND THEIR CORRESPONDING PARTICLE PICTURES Robert J.