Substitutions and Symbolic Dynamics

Marie-Pierre Béal is professor at Université Gustave Eiffel. She specialises in Symbolic Dynamics. Fabien Durand is professor at the Université de Picardie Jules Verne. He is co-author of Dimension Groups and Dynamical Systems (2022). He specialises in Symbolic Dynamics. Dominique Perrin is an Emeritus professor at Université Gustave Eiffel. He is the co-author of numerous works, including Codes and Automata (2013, CUP), Dimension Groups and Dynamical Systems (2022, CUP).

• Introduction; 1. Dynamical systems; 2. Shift spaces; 3. Substitutions; 4.Fixed points; 5. Morphic shifts; 6. Complexity of substitution shifts; 7. Numeration Systems; 8. Automatic sequences; 9. Recognizability; 10. Derivatives; 11. Periodicity; 12. Probability measures; 13. Disjointness theorems; 14. Hidden automatic sequences; 15. Topological full groups; 16. Spectral theory of substitution shifts; 17. Isomorphism of morphic shifts; A. Solutions to exercises; B. Useful definitions and results; C. Open problems; References; Name index; Subject index; Index of symbols.