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Ergodic Theory and Fractal Geometry

2014-08-08 Mathematics
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Release : 2014-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 346/5 ( reviews)

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Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg. This book was released on 2014-08-08. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.

Ergodic Theory and Fractal Geometry

2017-06-05 Mathematics
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Release : 2017-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 268/5 ( reviews)

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Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg. This book was released on 2017-06-05. Available in PDF, EPUB and Kindle. Book excerpt: fractal Geometry represents a radical departure from classical Geometry, which focuses on smooth objects that straighten out under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as zooming in. this zooming-in process has its parallels in dynamics, and the varying scenery corresponds to the evolution of dynamical variables. the present monograph focuses on applications of one branch of dynamics ergodic theory the Geometry of fractals. Much attention is given to the all-important notion of Fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of Fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics.

Ergodic Theory and Fractal Geometry

2014 Ergodic theory
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Release : 2014
Genre : Ergodic theory
Kind : eBook
Book Rating : 540/5 ( reviews)

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Book Synopsis Ergodic Theory and Fractal Geometry by : Harry Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Harry Furstenberg. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: "Notes based on a series of lectures delivered at Kent State University in 2011"--Preface.

Fractal Geometry and Analysis

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 318/5 ( reviews)

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Book Synopsis Fractal Geometry and Analysis by : Jacques Bélair

Download or read book Fractal Geometry and Analysis written by Jacques Bélair. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractal Geometry and Stochastics

2013-11-27 Mathematics
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Release : 2013-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 552/5 ( reviews)

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Book Synopsis Fractal Geometry and Stochastics by : Christoph Bandt

Download or read book Fractal Geometry and Stochastics written by Christoph Bandt. This book was released on 2013-11-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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