Abstract
The aim of this chapter is to introduce some concepts and to fix the notation we will use throughout this book. We will first introduce some terminology in combinatorics on words. These notions have their counterpart in terms of symbolic dynamics. We shall illustrate these definitions through the example of a particular sequence, the Morse sequence, generated by an algorithmic process we shall study in details in this book, namely a substitution. After recalling some basic notions on substitutions, we shall focus on the concept of automatic sequences. We then introduce the first notions of ergodic theory and focus on the spectral description of discrete dynamical systems.
This chapter has been written by V. Berthé and A. Siegel
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Basic notions on substitutions. In: Fogg, N.P., Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds) Substitutions in Dynamics, Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 1794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45714-3_1
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DOI: https://doi.org/10.1007/3-540-45714-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44141-0
Online ISBN: 978-3-540-45714-5
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