Topics in Ergodic Theory [Paperback]

An introduction to topics and examples of ergodic theory, a central area of pure mathematics.Since the 1930s ergodic theory has been central to pure mathematics. This introduction provides sections on the classical ergodic theorems, topological dynamics, uniform distribution, Martingales, information theory and entropy. There is a chapter on mixing and one on special examples.Since the 1930s ergodic theory has been central to pure mathematics. This introduction provides sections on the classical ergodic theorems, topological dynamics, uniform distribution, Martingales, information theory and entropy. There is a chapter on mixing and one on special examples.Ergodic theory grew out of an important problem of statistical mechanics which was resolved by Birkhoff and von Neumann in the 1930s. Since that time the subject has made its way to the centre of pure mathematics, drawing on the techniques of many other areas and, in turn, influencing those areas. The author has provided in this slim volume a speedy introduction to a considerable number of topics and examples. He includes sections on the classical ergodic theorems, topological dynamics, uniform distribution, Martingales, information theory and entropy. There is a chapter on mixing and one on special examples. The book concludes with an appendix on the spectral multiplicity theory of unitary operators.Preface; Introduction; 1. The principal ergodic theorems; 2. Martingales and the ergodic theorem of information theory; 3. Mixing; 4. Entropy; 5. Some examples; Appendix; References; Further literature; Index.