Chaotic Dynamics: Fractals, Tilings, and Substitutions Geoffrey R. Goodson's is an English-language textbook aimed at dynamical systems. This book offers a rigorous introduction to dynamical systems and is suitable for students moving from calculus to advanced mathematics.
The book serves as an accessible yet in-depth reference work with a clear structure. It covers, among other topics, topological and symbolic dynamics, two-dimensional dynamics, Sharkovsky's theorem, and substitution theory. Particular attention is given to Newton’s method, with extensive and carefully explained proofs.
Students benefit from a variety of exercises with increasing difficulty and hints, as well as concrete applications from real analysis and metric space theory. The Mathematica code available online supports understanding of the dynamical aspects.
This textbook aligns with courses such as differential calculus and differential equations and is used extensively in higher education. It is part of the Cambridge Mathematical Textbooks collection.