An exploration of dynamical systems and chaos

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This book serves as a comprehensive text on non-linear dynamical systems, focusing on chaotic phenomena. It is designed for both those wishing to study the physics of chaotic systems in depth and those simply curious about chaos. Fundamental concepts such as Poincaré sections, iterated mappings, Hamiltonian chaos, KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity, renormalization, and transitions to chaos are clearly explained. Mathematical concepts are introduced in concise sub-sections for better understanding. The text includes numerous computer experiments and a wealth of graphical illustrations and color plates that highlight the geometrical and topological features of the dynamics involved. This revised and expanded second edition incorporates recent research findings and adds a new section on basic probability theory. A new chapter on fully developed turbulence discusses the successes and limitations of chaos theory, along with future trends in complex spatio-temporal structures. Esteemed scholars have praised the book for its value in lectures and as a reference for the field of non-linear and chaotic systems, noting its unique reporting on scientific advancements and applications over recent decades.