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Lectures on Fractal Geometry and Dynamical Systems by Vaughn Climenhaga, Yakov Pesin (Paperback, 2009)

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Product Information

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.

Product Identifiers

Publisher
American Mathematical Society
ISBN-13
9780821848890
eBay Product ID (ePID)
91411178

Product Key Features

Author
Vaughn Climenhaga, Yakov Pesin
Publication Name
Lectures on Fractal Geometry and Dynamical Systems
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2009
Type
Textbook
Number of Pages
324 Pages

Additional Product Features

Title_Author
Vaughn Climenhaga, Yakov Pesin
Series Title
Student Mathematical Library
Country/Region of Manufacture
United States

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Lectures on Fractal Geometry and Dynamical Systems by Vaughn Climenhaga, Yakov Pesin (Paperback, 2009)

Best-selling in Adult Learning & University

Secrets Of Mental Math: The Mathemagician's Guide to Lightening Calculation and Amazing Maths Tricks by Arthur Benjamin, Michael Shermer (Paperback, 2006)

Never Split the Difference: Negotiating as if Your Life Depended on It by Chris Voss, Tahl Raz (Paperback, 2017)

Die with Zero: Getting All You Can from Your Money and Your Life by Bill Perkins (Paperback, 2021)

The Falsification of History: Our Distorted Reality by John Hamer (Paperback, 2013)

Adult Children of Emotionally Immature Parents: How to Heal from Distant, Rejecting, or Self-Involved Parents by Lindsay C Gibson (Paperback, 2015)

Code of Practice for In-service Inspection and Testing of Electrical Equipment by The Institution of Engineering and Technology (Paperback, 2020)

Clean & Green: 101 Hints and Tips for a More Eco-Friendly Home by Nancy Birtwhistle (Hardcover, 2021)

Save on Adult Learning & University

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Bold Beans: Beautiful, Brilliant and Exciting Recipes by Amelia Christie-Miller

The Concise Laws of Human Nature by Robert Greene Paperback, English

Zero to One: Notes on Start Ups, or How to Build the Future by Thiel, Peter The

Staring At The Sun: Being at peace with your own mortality by Irvin Yalom

Why We Get Sick (Paperback) by Bikman & Benjamin

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