Exceptional parameters of linear mod one transformations and fractional parts $ \{\xi {(p/q)}^{n}\}$

DoYong Kwon

doi:10.1016/j.crma.2015.01.017

Number theory

Exceptional parameters of linear mod one transformations and fractional parts

{ξ {(p / q)}^{n}}

[Paramètres exceptionnels de transformations linéaires mod un et parties fractionnaires

{ξ {(p / q)}^{n}}

]

Présenté par : the Editorial Board

DoYong Kwon ¹

¹ Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea

Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 291-296.

Résumé
Abstract

Nous étudions des paramètres exceptionnels de transformations linéaires mod un. La présente note prouve que l'ensemble de ces valeurs a zéro pour dimension de Hausdorff. Ceci répond à la question posée par Bugeaud.

We study exceptional parameters of linear mod one transformations. The present note proves that the set of such values has Hausdorff dimension zero. This answers the question posed by Bugeaud.

Reçu le : 2014-04-22
Accepté le : 2015-01-28
Publié le : 2015-02-11

DOI : 10.1016/j.crma.2015.01.017

Affiliations des auteurs :

DoYong Kwon ¹

¹ Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea

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DoYong Kwon. Exceptional parameters of linear mod one transformations and fractional parts $ \{\xi {(p/q)}^{n}\}$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 4, pp. 291-296. doi : 10.1016/j.crma.2015.01.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.01.017/

Bibliographie
Cité par

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[8] D.Y. Kwon The natural extensions of β-transformations which generalize Baker's transformations, Nonlinearity, Volume 22 (2009) no. 2, pp. 301-310

[9] D.Y. Kwon The orbit of a β-transformation cannot lie in a small interval, J. Korean Math. Soc., Volume 49 (2012) no. 4, pp. 867-879

[10] D.Y. Kwon Moments of discrete measures with dense jumps induced by β-expansions, J. Math. Anal. Appl., Volume 399 (2013) no. 1, pp. 1-11

[11] D.Y. Kwon A two-dimensional singular function via Sturmian words in base β, J. Number Theory, Volume 133 (2013) no. 11, pp. 3982-3994

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