With emphasis on stochastic aspects of deterministic systems this short book introduces the reader to the basic facts and some special topics of applied ergodic theory. It adresses advanced undergraduate and graduate students from various disciplines, i.e. mathematicians, physicists, electrical and mechanical engineers. Based upon a sound (but non-technical) mathematical introduction, a number of typical examples from applications (mostly from mechanics) are thoroughly discussed. By studying both probabilistic and deterministic features of dynamical systems the reader will develop what...

This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines up-to-date theoretical results with overviews of the law's colorful history, rapidly growing body of empirical evidence, and wide range of applications.

An Introduction to Benford's Law begins with basic facts about significant digits, Benford functions, sequences, and random variables,...