Encounters with chaos and fractals (Q2883332)

This text aims to introduce ``anyone who has a knowledge of calculus'' to ``chaotic dynamics and fractal geometry at a modest level of sophistication.'' Indeed, the author makes this possible through careful exposition, examples, and exercises presenting topics such as the Smale horseshoe map, the Lorenz system, dimension, and iterated function systems. Along the way the author familiarizes the student reader with more advanced background material such as the Cantor set, space-filling curves, Cauchy sequences, complete metric spaces, the Bolzano-Weierstrass theorem, and more.NEWLINENEWLINE The text is divided into the following chapters: 1. Periodic points; 2. One-dimensional chaos; 3. Two-dimensional chaos; 4. Systems of differential equations; 5. Introduction to fractals;NEWLINENEWLINE6. Creating fractal sets; 7. Complex fractals: Julia sets and the Mandelbrot set. {\noindent}Chapters 1--4 correspond to Chapters 1--3 and 5 of the original edition from 1992, while Chapters 5, 6, and 7 expand on Chapter 4 (``Fractals'') of the original edition. The Appendix contains ten computer programs for MATLAB (as opposed to TRUE BASIC in the original edition) including programs to produce the logistic family bifurcation diagram, the Hénon attractor, Julia sets, the Mandelbrot set, and the Barnsley fern leaf.