Substitutions in Dynamics, Arithmetics and Combinatorics

• Main Author: Pytheas Fogg, N. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Berthé, Valerie (Editor, http://id.loc.gov/vocabulary/relators/edt), Ferenczi, Sebastien (Editor, http://id.loc.gov/vocabulary/relators/edt), Mauduit, Christian (Editor, http://id.loc.gov/vocabulary/relators/edt), Siegel, Anne (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1794
• Subjects: Number theory.; Functions of real variables.; Dynamics.; Ergodic theory.; Sequences (Mathematics).; Computers.; Mathematical logic.; Number Theory.; Real Functions.; Dynamical Systems and Ergodic Theory.; Sequences, Series, Summability.; Computation by Abstract Devices.; Mathematical Logic and Formal Languages.
• Physical Description: XX, 404 p. online resource.
• ISBN: 9783540457145
• ISSN: 0075-8434 ;
• DOI: 10.1007/b13861

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.