Feldman D. Chaos and Fractals. An Elementary Introduction 2012 torrent

Textbook in PDF format

This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations. The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.
Contents
Introducing Discrete Dynamical Systems
Opening Remarks
Functions
Iterating Functions
Qualitative Dynamics
Time Series Plots
Graphical Iteration
Iterating Linear Functions
Population Models
Newton, Laplace, and Determinism
Chaos
Chaos and the Logistic Equation
The Buttery Effect
The Bifurcation Diagram
Universality
Statistical Stability of Chaos
Determinism, Randomness, and Nonlinearity
Fractals
Introducing Fractals
Dimensions
Random Fractals
The Box-Counting Dimension
When do Averages exist?
Power Laws and Long Tails
Introducing Julia Sets
Infinities, Big and Small
Julia Sets and The Mandelbrot Set
Introducing Julia Sets
Complex Numbers
Julia Sets for f(z) = z2 + c
The Mandelbrot Set
Higher-Dimensional Systems
Two-Dimensional Discrete Dynamical Systems
Cellular Automata
Introduction to Differential Equations
One-Dimensional Differential Equations
Two-Dimensional Differential Equations
Chaotic Differential Equations and Strange Attractors
Conclusion
Appendices