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More on the dynamics of the symbolic square root map

Julkaisun tekijät: Peltomäki Jarkko, Whiteland Markus
Julkaisuvuosi: 2017
Journal: Lecture Notes in Computer Science
Kirjan nimi *: Combinatorics on Words: 11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings
Sarjan nimi: Lecture Notes in Computer Science
Volyymi: 10432
ISBN: 978-3-319-66395-1
eISBN: 978-3-319-66396-8
ISSN: 0302-9743


In our earlier paper [A square root map on Sturmian words, Electron. J. Combin. (2017)], we introduced a symbolic square root map. Every optimal squareful infinite word $s$ contains exactly six minimal squares and can be written as a product of these squares: $s = X_1^2 X_2^2 cdots$. The square root $sqrt{s}$ of $s$ is the infinite word $X_1 X_2 cdots$ obtained by deleting half of each square. We proved that the square root map preserves the languages of Sturmian words (which are optimal squareful words). The dynamics of the square root map on a Sturmian subshift are well understood. In our earlier work, we introduced another type of subshift of optimal squareful words which together with the square root map form a dynamical system. In this paper, we study these dynamical systems in more detail and compare their properties to the Sturmian case. The main results are characterizations of periodic points and the limit set. The results show that while there is some similarity it is possible for the square root map to exhibit quite different behavior compared to the Sturmian case.

Last updated on 2019-21-08 at 20:01