Measure, Topology, and Fractal Geometry
Author: Gerald A. Edgar
Publisher:
Published: 2014-01-15
Total Pages: 256
ISBN-13: 9781475741353
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Measure, Topology, and Fractal Geometry
Author: Gerald Edgar
Publisher: Springer Science & Business Media
Published: 2007-10-23
Total Pages: 293
ISBN-13: 0387747494
DOWNLOAD EBOOK →Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.
Measure, Topology, and Fractal Geometry
Author: Gerald A. Edgar
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 252
ISBN-13: 1475741340
DOWNLOAD EBOOK →From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1
Measure, Topology, and Fractal Geometry
Author: Gerald Edgar
Publisher: Springer
Published: 2008-11-01
Total Pages: 0
ISBN-13: 9780387521008
DOWNLOAD EBOOK →Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.
The Geometry of Fractal Sets
Author: K. J. Falconer
Publisher: Cambridge University Press
Published: 1985
Total Pages: 184
ISBN-13: 9780521337052
DOWNLOAD EBOOK →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.
Integral, Probability, and Fractal Measures
Author: Gerald A. Edgar
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 292
ISBN-13: 1475729588
DOWNLOAD EBOOK →Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.
Fractals in Probability and Analysis
Author: Christopher J. Bishop
Publisher: Cambridge University Press
Published: 2017
Total Pages: 415
ISBN-13: 1107134110
DOWNLOAD EBOOK →A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Fractal Geometry and Stochastics VI
Author: Uta Freiberg
Publisher: Springer Nature
Published: 2021-03-23
Total Pages: 307
ISBN-13: 3030596494
DOWNLOAD EBOOK →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.
Geometry of Sets and Measures in Euclidean Spaces
Author: Pertti Mattila
Publisher: Cambridge University Press
Published: 1999-02-25
Total Pages: 360
ISBN-13: 9780521655958
DOWNLOAD EBOOK →This book studies the geometric properties of general sets and measures in euclidean space.
Lectures on Fractal Geometry and Dynamical Systems
Author: Ya. B. Pesin
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 334
ISBN-13: 0821848895
DOWNLOAD EBOOK →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.
