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Fractal Geometry

Mathematical Foundations and Applications

$Falconer covers the general theory of fractals and their geometry, providing exercises as well as illustrated examples. Results are stated precisely but technical measure theoretic ideas are avoided and difficult proofs are sketched.$

جزئیات و درخواست

By Kenneth Falconer
Publisher: John Wiley & Sons, 1997-05-05
Pages: 288
Language: en
ISBN_10:0471967777
ISBN_13:9780471967774
Subject: Mathematics

Fractals: A Very Short Introduction

$Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.$

جزئیات و درخواست

By Kenneth Falconer
Publisher: OUP Oxford, 2013-09-26
Pages: 153
Language: en
ISBN_13:9780191663444
ISBN_10:0191663441
Subject: Mathematics

Techniques in Fractal Geometry

$Following on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals. Much of the material presented in this book has come to the fore in recent years. This includes methods for studying dimensions and other parameters of fractal sets and measures, as well as more sophisticated techniques such as thermodynamic formalism and tangent measures. In addition to general theory, many examples and applications are described, in areas such as differential equations and harmonic analysis. This book is mathematically precise, but aims to give an intuitive feel for the subject, with underlying concepts described in a clear and accessible manner. The reader is assumed to be familiar with material from Fractal Geometry, but the main ideas and notation are reviewed in the first two chapters. Each chapter ends with brief notes on the development and current state of the subject. Exercises are included to reinforce the concepts. The author's clear style and up-to-date coverage of the subject make this book essential reading for all those who with to develop their understanding of fractal geometry.$

جزئیات و درخواست

By Kenneth Falconer
Publisher: Wiley, 1997-05-28
Language: en
ISBN_10:0471957240
ISBN_13:9780471957249
Subject: Mathematics

Fractal Geometry

Mathematical Foundations and Applications

$Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0 Please click here to download solutions to exercises found within this title: http://www.wileyeurope.com/fractal$

جزئیات و درخواست

By Kenneth Falconer
Publisher: John Wiley & Sons, 2007-12-10
Pages: 367
Language: en
ISBN_13:9780470299456
ISBN_10:0470299452
Subject: Mathematics

Unsolved Problems in Geometry

جزئیات و درخواست

By Hallard T. Croft, K. J. Falconer, Richard K. Guy
Publisher: New York : Springer-Verlag, 1991
Pages: 224
Language: en
OTHER:UOM:49015001318923
Subject: Mathematics

The Geometry of Fractal Sets

$A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.$

جزئیات و درخواست

By K. J. Falconer
Publisher: Cambridge University Press, 1985
Pages: 184
Language: en
ISBN_10:0521337054
ISBN_13:9780521337052
Subject: Mathematics

Unsolved Problems in Geometry

Unsolved Problems in Intuitive Mathematics

جزئیات و درخواست

By Hallard T. Croft, Kenneth Falconer, Richard K. Guy
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 213
Language: en
ISBN_13:9781461209638
ISBN_10:1461209633
Subject: Mathematics

Assouad Dimension and Fractal Geometry

$The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.$

جزئیات و درخواست

By Jonathan M. Fraser
Publisher: Cambridge University Press, 2020-10-29
Pages: 287
Language: en
ISBN_13:9781108478656
ISBN_10:1108478654
Subject: Mathematics

Fractal Geometry and Stochastics V

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

جزئیات و درخواست

By Christoph Bandt, Kenneth Falconer, Martina Zähle
Publisher: Birkhäuser, 2015-07-08
Pages: 339
Language: en
ISBN_13:9783319186603
ISBN_10:3319186604
Subject: Mathematics

The Mathematical Coloring Book

Mathematics of Coloring and the Colorful Life of its Creator...

جزئیات و درخواست

By Alexander Soifer
Publisher: Springer Science & Business Media, 2008-10-13
Pages: 619
Language: en
ISBN_13:9780387746425
ISBN_10:0387746420
Subject: Mathematics

Geometry of Sets and Measures in Euclidean Spaces

Fractals and Rectifiability

جزئیات و درخواست

By Pertti Mattila
Publisher: Cambridge University Press, 1999-02-25
Pages: 360
Language: en
ISBN_10:0521655951
ISBN_13:9780521655958
Subject: Mathematics

Fractal Geometry

Mathematical Foundations and Applications

$An accessible introduction to fractals, useful as a text or reference. Part I is concerned with the general theory of fractals and their geometry, covering dimensions and their methods of calculation, plus the local form of fractals and their projections and intersections. Part II contains examples of fractals drawn from a wide variety of areas of mathematics and physics, including self-similar and self-affine sets, graphs of functions, examples from number theory and pure mathematics, dynamical systems, Julia sets, random fractals and some physical applications. Also contains many diagrams and illustrative examples, includes computer drawings of fractals, and shows how to produce further drawings for themselves.$

جزئیات و درخواست

By K. J. Falconer
1990-03-30
Pages: 318
Language: en
OTHER:UOM:39015049074639
Subject: Mathematics

Self-similar and Self-affine Sets and Measures

$Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.$

جزئیات و درخواست

By Balázs Bárány, Károly Simon, Boris Solomyak
Publisher: American Mathematical Society, 2023-11-16
Pages: 466
Language: en
ISBN_13:9781470470463
ISBN_10:1470470462
Subject: Mathematics

The Lighter Side of Mathematics: Proceedings of the Eugene Strens Memorial Conference on Recreational Mathematics and Its History

جزئیات و درخواست

By Richard K. Guy, Robert E. Woodrow
Publisher: American Mathematical Soc., 2020-08-03
Pages: 379
Language: en
ISBN_13:9781470457310
ISBN_10:1470457318
Subject: Mathematics

Fractal Geometry in Digital Imaging

$This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.$

جزئیات و درخواست

By Martin J. Turner, Jonathan M. Blackledge, Patrick R. Andrews
Publisher: Academic Press, 1998-06-23
Pages: 352
Language: en
ISBN_10:0127039708
ISBN_13:9780127039701
Subject: Computers

Probabilistic and Stochastic Methods in Analysis, with Applications

جزئیات و درخواست

By J.S. Byrnes, Kathryn A. Hargreaves, Karl Berry
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 688
Language: en
ISBN_13:9789401127912
ISBN_10:9401127913
Subject: Mathematics

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Fractals in Applied Mathematics

$This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.$

جزئیات و درخواست

By David Carfi, Michel L. Lapidus, Erin P. J. Pearse, Machiel van Frankenhuijsen
Publisher: American Mathematical Soc., 2013-10-24
Pages: 384
Language: en
ISBN_13:9780821891483
ISBN_10:0821891480
Subject: Mathematics

Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries

جزئیات و درخواست

By Joseph D. E. Konhauser, Dan Velleman, Stan Wagon
Publisher: American Mathematical Soc., 1996-12-31
Pages: 258
Language: en
ISBN_13:9781470463823
ISBN_10:1470463822
Subject: Education

Geometry and Analysis of Fractals

Hong Kong, December 2012

$This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.$

جزئیات و درخواست

By De-Jun Feng, Ka-Sing Lau
Publisher: Springer, 2014-08-01
Pages: 360
Language: en
ISBN_13:9783662439203
ISBN_10:3662439204
Subject: Mathematics

The New Mathematical Coloring Book

Mathematics of Coloring and the Colorful Life of Its Creator...

جزئیات و درخواست

By Alexander Soifer
Publisher: Springer Nature,
Pages: 838
Language: en
ISBN_13:9781071635971
ISBN_10:1071635972

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