Geodesic
Numbers with Almost all Convergents in a Cantor Set
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 869-875

Voir la notice de l'article provenant de la source Cambridge University Press

In 1984, K. Mahler asked how well elements in the Cantor middle third set can be approximated by rational numbers from that set and by rational numbers outside of that set. We consider more general missing digit sets $C$ and construct numbers in $C$ that are arbitrarily well approximable by rationals in $C$, but badly approximable by rationals outside of $C$. More precisely, we construct them so that all but finitely many of their convergents lie in $C$.
DOI : 10.4153/S0008439518000450
Mots-clés : Cantor set, continued fraction, Diophantine approximation, parametric geometry of numbers 
Roy, Damien; Schleischitz, Johannes. Numbers with Almost all Convergents in a Cantor Set. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 869-875. doi: 10.4153/S0008439518000450
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