Substitutions and Symbolic Dynamics

The first comprehensive survey of sequences and shift spaces defined by substitutions, featuring results, full proofs, and exercises.

The first comprehensive introduction of survey of sequences and shift spaces defined by substitutions. The text covers all significant results on the subject with full proofs, and each chapter is supplemented with exercises. It is suitable as a reference for graduate students and academic researchers in dynamical systems.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.