Fractal Geometry And Stochastics Iv

Author : Christoph Bandt,Peter Mörters,Martina Zähle
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 53,9 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 : Christoph Bandt,Peter Mörters,Martina Zähle
Publisher : Birkhäuser
Page : 290 pages
File Size : 45,8 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 : Uta Freiberg,Ben Hambly,Michael Hinz,Steffen Winter
Publisher : Springer Nature
Page : 307 pages
File Size : 54,9 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 : 286 pages
File Size : 46,5 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,Kenneth Falconer,Martina Zähle
Publisher : Birkhäuser
Page : 340 pages
File Size : 40,9 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,Siegfried Graf,Martina Zähle
Publisher : Birkhäuser
Page : 248 pages
File Size : 51,6 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 : Kenneth Falconer
Publisher : John Wiley & Sons
Page : 457 pages
File Size : 51,5 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9781118762868

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Fractal Geometry by Kenneth Falconer Pdf

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applications of fractals in a way that is accessible to students and researchers from a wide range of disciplines. Fractal Geometry: Mathematical Foundations and Applications is an excellent course book for undergraduate and graduate students studying fractal geometry, with suggestions for material appropriate for a first course indicated. The book also provides an invaluable foundation and reference for researchers who encounter fractals not only in mathematics but also in other areas across physics, engineering and the applied sciences. Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals Carefully explains each topic using illustrative examples and diagrams Includes the necessary mathematical background material, along with notes and references to enable the reader to pursue individual topics Features a wide range of exercises, enabling readers to consolidate their understanding Supported by a website with solutions to exercises and additional material http://www.wileyeurope.com/fractal Leads onto the more advanced sequel Techniques in Fractal Geometry (also by Kenneth Falconer and available from Wiley)

Author : Christoph Bandt
Publisher : Unknown
Page : 292 pages
File Size : 41,5 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 : Birkhäuser
Page : 272 pages
File Size : 53,5 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 : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 312 pages
File Size : 44,9 Mb
Release : 2017-08-23
Category : Mathematics
ISBN : 9783319578057

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Recent Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

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.

Author : Michael Falk,Jürg Hüsler,Rolf-Dieter Reiss
Publisher : Birkhäuser
Page : 381 pages
File Size : 41,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034877916

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Laws of Small Numbers: Extremes and Rare Events by Michael Falk,Jürg Hüsler,Rolf-Dieter Reiss Pdf

Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.

Author : Patricia Alonso Ruiz,Joe Po-chou Chen,Luke G Rogers,Alexander Teplyaev
Publisher : World Scientific
Page : 594 pages
File Size : 41,8 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 : Martina Zaehle
Publisher : World Scientific
Page : 141 pages
File Size : 48,6 Mb
Release : 2023-12-27
Category : Mathematics
ISBN : 9789811283352

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Lectures On Fractal Geometry by Martina Zaehle Pdf

This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.

Author : Christoph Bandt,Umberto Mosco,Martina Zähle
Publisher : Birkhäuser
Page : 265 pages
File Size : 41,9 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 : Daniel Lenz,Florian Sobieczky,Wolfgang Woess
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 52,6 Mb
Release : 2011-06-16
Category : Mathematics
ISBN : 9783034602440

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Random Walks, Boundaries and Spectra by Daniel Lenz,Florian Sobieczky,Wolfgang Woess Pdf

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.