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Download An Introduction to Chaotic Dynamical Systems, 2nd Edition eBook

by Robert Devaney,Robert L. Devaney

Download An Introduction to Chaotic Dynamical Systems, 2nd Edition eBook
ISBN:
0813340853
Author:
Robert Devaney,Robert L. Devaney
Category:
Mathematics
Language:
English
Publisher:
CRC Press; 2 edition (January 2003)
Pages:
360 pages
EPUB book:
1382 kb
FB2 book:
1816 kb
DJVU:
1655 kb
Other formats
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Rating:
4.3
Votes:
483


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This book is an introduction to dynamical systems defined by iterative maps of continuous functions. It doesn't require much advanced knowledge, but it does require a familiarity and certain level of comfort with proofs. The basic idea of this book is to explore (in the context of iterative maps) the major themes of dynamical systems, which can later be explored in the messier setting of differential equations and continuous-time systems

Robert Devaney, Robert L. Devaney.

Robert Devaney, Robert L.

Поиск книг BookFi BookSee - Download books for free. A First Course In Chaotic Dynamical Systems: Theory And Experiment (Studies in Nonlinearity).

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has . He is the author of An Introduction to Chaotic Dynamical Systems, and Chaos, Fractals, and Dynamics: Computer Experiments in Modern Mathematics, which aims to explain the beauty of chaotic dynamics to high school students and teachers.

Robert Luke Devaney (born 1948) is an American mathematician, the Feld Family Professor of Teaching Excellence at Boston University. Devaney was born on April 9, 1948, and grew up in Methuen, Massachusetts. Devaney graduated in 1969 from the College of the Holy Cross, and earned his P. in 1973 from the University of California, Berkeley under the supervision of Stephen Smale.

Part One: One-Dimensional Dynamics . Examples of dynamical systems . Preliminaries from calculus . Elementary definitions . Hyperbolicity . An example: the quadratic family . Symbolic dynamics . Topological conjugacy . Chaos. Structural stability . 0 Sarkovskii's theorem . 1.

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The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
  • Uylo
Classic textbook. The level of exposition is perhaps suitable for an undergraduate mathematics class for advanced students. The textbooks focuses on *discrete-time systems* (maps), so an undergraduate introductory course on dynamical systems which aims at presenting a balanced set of topics on discrete and continuous-time systems, may perhaps use parts of this textbook and complement with Strogatz's Nonlinear Dynamics and Chaos to study continuous-time systems as well.
  • September
It's very good.
  • Kalv
Thank You.
  • thrust
Excellent book for an introductory course in the subject.
  • Ieslyaenn
Great introduction book to the theme. Easy to read and with good practical exercises.
  • TheSuspect
This is a very good book. Actually, Devaney's "First Course in Chaotic Dynamical Systems," is a good accompanying text. Fascinating subject...
  • Lavivan
Great Product in less amount of Money.
This book is an introduction to dynamical systems defined by iterative maps of continuous functions. It doesn't require much advanced knowledge, but it does require a familiarity and certain level of comfort with proofs. The basic idea of this book is to explore (in the context of iterative maps) the major themes of dynamical systems, which can later be explored in the messier setting of differential equations and continuous-time systems. While this book doesn't discuss differential equations directly, the techniques used here can be transferred (with considerable work and thought) to that setting. Someone wanting an elementary book covering differential equations as dynamical systems might want to check out the excellent multi-volume work by J. Hubbard; the combination of that work with this book would provide the background to tackle the tougher and less-accessible texts dealing with chaotic systems of differential equations.

Although this is a pure math book, the book does mention key applications and motivation behind the material; applied mathematicians will find this book quite useful, not necessarily because of the choice of topics but just because it greatly helps develop ones' intuition. The material is presented in a way that gives the student a sense of the big picture--what the theorems mean, how they fit together. Proofs are rigorous but as easy to follow as I have seen them in this subject.

The choice and order of subjects is also both practical and fun. The book begins with 1-dimensional systems and explores just about everything interesting that happens with them (including Sarkovski's Theorem, one of the most bizarre and surprising mathematical results), before moving into two-dimensions and then dynamics in the complex plane.

The bottom line? This book would be excellent both as a textbook and for self-study. If you're interested in this subject at all, this is a book you will want on your shelf. I know of no other book on the subject that covers such deep material while remaining as accessible.