Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.
A First Course in Discrete Dynamical Systems
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Most Helpful Customer Reviews
5.0 out of 5 stars
Amazing motivational introduction,
This review is from: A First Course in Discrete Dynamical Systems (Universitext) (Paperback)
An excellent short motivational reading / introductory course material. Starts ground up and uses very simple hands-on examples to demonstrate the fascinating behavior of non-linear dynamic systems (chaos, fractals, etc). Covers most of the basic methodology.The book also has a lot of excellent exercises for reinforcing the material, for different difficulty levels.
0 of 2 people found the following review helpful:
5.0 out of 5 stars
An excellent book,
By E.Ahmed (Egypt) - See all my reviews
This review is from: A First Course in Discrete Dynamical Systems (Universitext) (Paperback)
This is an excellent book for teaching for mathematics students. Besides the standard material it contains a chapter about some numerical methods as dynamical systems. I strongly propose that a third updated edition is made.
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Inside This Book
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First Sentence:
A discrete dynamical system can be characterized as a function that is composed with itself over and over again. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
periodic point with prime period, attracting periodic point, complex quadratic polynomials, repelling set, differentiable complex function, topological conjugacy, attracting fixed point, repelling fixed point, repelling periodic point, hyperbolic periodic point, periodic points, many iterates, attracting orbit, period two orbit, correct qualitative behavior, exhibits sensitive dependence, attracting periodic orbit, doubling map, topological conjugacies, topological transitivity, shift map, stable set, extended complex plane, only fixed point, accumulation point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Set, Intermediate Value Theorem, Mean Value Theorem, Triangle Inequality, Prove Proposition, Chaotic Dynamical Systems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A discrete dynamical system can be characterized as a function that is composed with itself over and over again. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
periodic point with prime period, attracting periodic point, complex quadratic polynomials, repelling set, differentiable complex function, topological conjugacy, attracting fixed point, repelling fixed point, repelling periodic point, hyperbolic periodic point, periodic points, many iterates, attracting orbit, period two orbit, correct qualitative behavior, exhibits sensitive dependence, attracting periodic orbit, doubling map, topological conjugacies, topological transitivity, shift map, stable set, extended complex plane, only fixed point, accumulation point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Set, Intermediate Value Theorem, Mean Value Theorem, Triangle Inequality, Prove Proposition, Chaotic Dynamical Systems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 80
books:
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95
books
cite this book:
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- An Introduction to Chaotic Dynamical Systems, 2nd Edition by Robert Devaney on 5 pages
- Dynamical Systems: Stability, Symbolic Dynamics, and Chaos (Studies in Advanced Mathematics) by Clark Robinson on 5 pages
- The Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin on page 26, page 57, and Back Matter
- Chaos and Fractals: New Frontiers of Science by Heinz-Otto Peitgen on page 107, page 197, and Back Matter
- General Topology (Dover Books on Mathematics) by Stephen Willard on page 17, and Back Matter
See all 80 books this book cites
- Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) by John Banks on 5 pages
- Mathematical Methods: for Students of Physics and Related Fields (Undergraduate Texts in Contemporary Physics) by Sadri Hassani in Back Matter (1), and Back Matter (2)
- p-adic Numbers: An Introduction (Universitext) by Fernando Quadros Gouvea in Back Matter
- Logic and Structure by Dirk van Dalen in Back Matter
- A Course in Credibility Theory and its Applications (Universitext) by Hans Bühlmann in Back Matter
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