Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena focuses on explaining the fundamentals of the subject by studying examples from one-dimensional maps and simple differential equations. The book includes numerous line diagrams and computer graphics as well as problems and solutions to test readers' understanding.
The book is written primarily for advanced undergraduate students in science yet postgraduate students and researchers in mathematics, physics, and other areas of science will also find the book useful.
WHAT IS CHAOS? Characteristics of chaos Chaos in nature LI-YORKE CHAOS, TOPOLOGICAL ENTROPY, AND LYAPUNOV NUMBER Li-Yorke theorem and Sharkovski theorem: Li-Yorke's theorem Sharkovski's theorem Periodic orbits: Number of periodic orbits Stability of orbits Li-Yorke theorem (continued) Scrambled set and observability of Li-Yorke chaos: Nathanson's example Observability of Li-Yorke chaos Topological entropy Density of orbits: Observable chaos and Lyapunov number Denseness of orbits Invariant measure Lyapunov number Summary ROUTE TO CHAOS Pitchfork bifurcation and Feigenbaum route Conditions for pitchfork bifurcation Windows Intermittent chaos CHAOS IN REALISTIC SYSTEMS Conservative system and dissipative system Attractors and Poincare section Lyapunov numbers and change of volume Construction of attractor Hausdorff dimension, generalized dimension and fractal Evaluation of correlation dimension Evaluation of Lyapunov number Global spectrum-the If(a) method APPENDICES Periodic solutions of the logistic map Mobius function and inversion formula Countable sets and uncountable sets Upper limit and lower limit Lebsgue measure Normal numbers Periodic orbits with finite fraction initial value The delta-function Where does period 3 window begin in logistic map? Newton method How to evaluate topological entropy Examples of invariant measure Generalized dimension Dq is monotonically decreasing in q Saddle point method Chaos in double-pendulum Singular points and limit cycle of van der Pol Equation Singular points of the Rossler model REFERENCES SOLUTIONS INDEX