Fabien Durand – författare

Substitutions play a role in many problems, such as combinatorics on words, linear recurrent sequences, numeration systems, and complexity theory. This text offers a unified treatment of these problems and easy access to the results and methods of proof. It presents a comprehensive survey of sequences and shift spaces defined by substitutions. The book covers important results, such as the finiteness theorem for minimal morphic shifts, which characterizes a minimal morphic shift by the finiteness of its set of derivatives. Other highlights include the proof of the recognizability property under very general assumptions and the classification of complexity types for substitution shifts. The work culminates with the proof of the decidability of conjugacy for minimal morphic shifts. This is an essential resource for graduate students and academic researchers in dynamical systems.

This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition - with full proofs - of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.