Grammatical Complexity and One-Dimensional Dynamical Systems (Directions in Chaos)

A combinatorial method is developed in this text to explore the mysteries of chaos, which has become a topic of science since 1975. Using tools from theoretical computer science, formal languages and automata, the complexity of symbolic behaviours of dynamical systems is classified and analyzed thoroughly. This book is mainly devoted to explanation of this method and its application to one-dimensional dynamical systems, including the circle and interval maps, which are typical in exihibiting complex behaviour through simple iterated calculations.