Problems and solutions. Nonlinear dynamics, chaos and fractals (Q5890630)

This is a very useful book for introductory courses in nonlinear dynamics, chaos and fractals.NEWLINENEWLINEIn Chapter 1, one-dimensional maps are introduced. Fixed points, periodic points and their stability play the central role in this chapter as well as the linearized equation. Exercises for chaotic maps such as the logistic map, tent map, Bernoulli map are provided. The Liapunov exponent, which characterizes chaos, is introduced. Problems for the linearization of nonlinear maps as well as invariants are provided. Exercises for the Newton map are also introduced. A number of problems deal with ergodic theory and the Frobenius-Perron integral equation. In Chapter 2, two-dimensional and higher-dimensional maps are covered as well as complex maps. Exercises for both invertible and noninvertible maps are provided. The Newton map is also covered. Some applications to differential forms are introduced. Chapter 3 is devoted to fractals, where fractal dimensions play a central role. For fractals, iterated functions systems are at the core of the construction. The Kronecker product is also introduced for the construction of fractals. Exercises cover the Cantor set, Sierpinski triangle, Sierpinski carpet, Koch curve, Menger sponge, etc. Many problems deal with the Mandelbrot and Julia sets. For some solutions of the problems, software such as C++, SymbolicC++, Maxima and R are utilized.NEWLINENEWLINEThis book does not go into deep concepts in bifurcation. It also does not relate Julia sets to complex maps and chaos. But these topics can be covered in more advanced courses. The reviewer thanks the author for this book and hopes that soon, a similar book will appear on the important topic of networks which deserves to be taught at the elementary level and not only at the advanced one.