Fractal Geometry And Stochastics V

Author : Christoph Bandt,Kenneth Falconer,Martina Zähle
Publisher : Birkhäuser
Page : 340 pages
File Size : 47,6 Mb
Release : 2015-07-08
Category : Mathematics
ISBN : 9783319186603

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Fractal Geometry and Stochastics V by Christoph Bandt,Kenneth Falconer,Martina Zähle Pdf

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.

Author : Christoph Bandt,Peter Mörters,Martina Zähle
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 44,8 Mb
Release : 2010-01-08
Category : Mathematics
ISBN : 9783034600309

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Fractal Geometry and Stochastics IV by Christoph Bandt,Peter Mörters,Martina Zähle Pdf

Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.

Author : Uta Freiberg,Ben Hambly,Michael Hinz,Steffen Winter
Publisher : Springer Nature
Page : 307 pages
File Size : 46,9 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030596491

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Fractal Geometry and Stochastics VI by Uta Freiberg,Ben Hambly,Michael Hinz,Steffen Winter Pdf

This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.

Author : Christoph Bandt,Siegfried Graf,Martina Zähle
Publisher : Birkhäuser
Page : 248 pages
File Size : 50,9 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9783034877558

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Fractal Geometry and Stochastics by Christoph Bandt,Siegfried Graf,Martina Zähle Pdf

Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.

Author : Christoph Bandt,Siegfried Graf,Martina Zähle
Publisher : Birkhäuser
Page : 286 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883801

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Fractal Geometry and Stochastics II by Christoph Bandt,Siegfried Graf,Martina Zähle Pdf

A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.

Author : Christoph Bandt
Publisher : Unknown
Page : 292 pages
File Size : 53,9 Mb
Release : 2000
Category : Fractals
ISBN : 0817662154

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Fractal Geometry and Stochastics II by Christoph Bandt Pdf

Author : Christoph Bandt,Siegfried Graf,Martina Zähle
Publisher : Birkhauser
Page : 245 pages
File Size : 52,8 Mb
Release : 1995
Category : Mathematics
ISBN : 0817652639

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Fractal Geometry and Stochastics by Christoph Bandt,Siegfried Graf,Martina Zähle Pdf

Author : Christoph Bandt,Peter Mörters,Martina Zähle
Publisher : Birkhäuser
Page : 290 pages
File Size : 45,6 Mb
Release : 2010-10-22
Category : Mathematics
ISBN : 303460033X

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Fractal Geometry and Stochastics IV by Christoph Bandt,Peter Mörters,Martina Zähle Pdf

Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.

Author : Christoph Bandt,Siegfried Graf,Martina Zähle
Publisher : Birkhäuser
Page : 248 pages
File Size : 48,6 Mb
Release : 1995-11-13
Category : Mathematics
ISBN : 3764352639

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Fractal Geometry and Stochastics by Christoph Bandt,Siegfried Graf,Martina Zähle Pdf

Fractal geometry is a new and promising field for researchers from different disciplines such as mathematics, physics, chemistry, biology and medicine. It is used to model complicated natural and technical phenomena. The most convincing models contain an element of randomness so that the combination of fractal geometry and stochastics arises in between these two fields. It contains contributions by outstanding mathematicians and is meant to highlight the principal directions of research in the area. The contributors were the main speakers attending the conference "Fractal Geometry and Stochastics" held at Finsterbergen, Germany, in June 1994. This was the first international conference ever to be held on the topic. The book is addressed to mathematicians and other scientists who are interested in the mathematical theory concerning: • Fractal sets and measures • Iterated function systems • Random fractals • Fractals and dynamical systems, and • Harmonic analysis on fractals. The reader will be introduced to the most recent results in these subjects. Researchers and graduate students alike will benefit from the clear expositions.

Author : Christoph Bandt,Umberto Mosco,Martina Zähle
Publisher : Birkhäuser
Page : 265 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878913

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Fractal Geometry and Stochastics III by Christoph Bandt,Umberto Mosco,Martina Zähle Pdf

This up-to-date monograph, providing an up-to-date overview of the field of Hepatitis Prevention and Treatment, includes contributions from internationally recognized experts on viral hepatitis, and covers the current state of knowledge and practice regarding the molecular biology, immunology, biochemistry, pharmacology and clinical aspects of chronic HBV and HCV infection. The book provides the latest information, with sufficient background and discussion of the literature to benefit the newcomer to the field.

Author : Peter Grabner,Wolfgang Woess
Publisher : Birkhäuser
Page : 288 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880145

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Fractals in Graz 2001 by Peter Grabner,Wolfgang Woess Pdf

This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in the second week of June 2001 at Graz University of Technology, in the capital of Styria, southeastern province of Austria. The scientific committee of the meeting consisted of M. Barlow (Vancouver), R. Strichartz (Ithaca), P. Grabner and W. Woess (both Graz), the latter two being the local organizers and editors of this volume. We made an effort to unite in the conference as well as in the present pro ceedings a multitude of different directions of active current work, and to bring together researchers from various countries as well as research fields that all are linked in some way with the modern theory of fractal structures. Although (or because) in Graz there is only a very small group working on fractal structures, consisting of "non-insiders", we hope to have been successful with this program of wide horizons. All papers were written upon explicit invitation by the editors, and we are happy to be able to present this representative panorama of recent work on poten tial theory, random walks, spectral theory, fractal groups, dynamic systems, fractal geometry, and more. The papers presented here underwent a refereeing process.

Author : De-Jun Feng,Ka-Sing Lau
Publisher : Springer
Page : 360 pages
File Size : 43,7 Mb
Release : 2014-08-01
Category : Mathematics
ISBN : 9783662439203

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Geometry and Analysis of Fractals by De-Jun Feng,Ka-Sing Lau Pdf

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.

Author : Jacques Bélair,Serge Dubuc
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 44,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401579315

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Fractal Geometry and Analysis by Jacques Bélair,Serge Dubuc Pdf

This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion on piecewise estimates yielding actual values for the most common dimensions (Hausdorff, box-counting and packing dimensions). The dimension theory is mainly discussed by Mendes-France, Bedford, Falconer, Tricot and Rata. Construction of fractal sets. Scale in variance is a fundamental property of fractal sets.

Author : Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev
Publisher : World Scientific
Page : 594 pages
File Size : 47,6 Mb
Release : 2020-02-26
Category : Mathematics
ISBN : 9789811215544

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Analysis, Probability And Mathematical Physics On Fractals by Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev Pdf

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.

Author : Ya. B. Pesin,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 46,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848890

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Lectures on Fractal Geometry and Dynamical Systems by Ya. B. Pesin,Vaughn Climenhaga Pdf

Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.