Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists
Mance, B; Tseng, J
Date: 2013
Journal
Acta Arithmetica
Publisher
Polskiej Akademii Nauk, Instytut Matematyczny
Publisher DOI
Abstract
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 ...
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).
Mathematics and Statistics
Faculty of Environment, Science and Economy
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