Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists
Polskiej Akademii Nauk, Instytut Matematyczny
We show that the set of numbers with bounded L uroth expansions (or bounded L uroth series) is winning and strong winning. From either winning property, it immediately follows that the set is dense, has full Hausdor dimension, and satis es a countable intersection property. Our result matches the well-known analogous result for bounded continued fraction expansions or, equivalently, badly approximable numbers. We note that L uroth expansions have a countably in nite Markov partition, which leads to the notion of in nite distortion (in the sense of Markov partitions).
This is the author accepted manuscript. The final version is available from Polskiej Akademii Nauk, Instytut Matematyczny via the DOI in this record.
Vol. 158, pp. 33 - 47