Comptes Rendus
Combinatorics, Dynamical systems
The critical exponent functions
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 315-332.

The critical exponent of a finite or infinite word w over a given alphabet is the supremum of the reals α for which w contains an α-power. We study the maps associating to every real in the unit interval the inverse of the critical exponent of its base-n expansion. We strengthen a combinatorial result by J.D. Currie and N. Rampersad to show that these maps are left- or right-Darboux at every point, and use dynamical methods to show that they have infinitely many nontrivial fixed points and infinite topological entropy. Moreover, we show that our model-case map is topologically mixing.

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DOI: 10.5802/crmath.286
Classification: 37B40, 37B20, 68R15, 26A21, 26A18
Dario Corona 1; Alessandro Della Corte 2

1 University of Camerino, School of Science and Technology Camerino (MC), Italy
2 University of Camerino,School of Science and Technology, Camerino (MC), Italy
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Dario Corona; Alessandro Della Corte. The critical exponent functions. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 315-332. doi : 10.5802/crmath.286. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.286/

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