2012/02/18 by Bill Mance, Mance, Bill, Jimmy Tseng +1 · 1 citation
Mathematics · #11J70 #11K55 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11J70 #msc:11K55 #msc:37E05
paper · pdf · doi:10.48550/arxiv.1202.4109
15 pages. No changes to the proof. Very minor changes in the exposition
arxiv created 2012/10/24 · arxiv updated 2012/10/25
We show that the set of numbers with bounded Lüroth expansions (or bounded Lüroth series) is winning and strong winning. From either winning property, it immediately follows that the set is dense, has full Hausdorff dimension, and satisfies 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 Lüroth expansions have a countably infinite Markov partition, which leads to the notion of infinite distortion (in the sense of Markov partitions).