Geodesic
Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists
Bill Mance 1   ; Jimmy Tseng 2
1 Department of Mathematics Ohio State University Columbus, OH 43210, U.S.A.
2 Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, U.S.A.
Acta Arithmetica, Tome 158 (2013) no. 1, pp. 33-47 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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).
DOI : 10.4064/aa158-1-2
Keywords: set numbers bounded roth expansions bounded roth series winning strong winning either winning property immediately follows set dense has full hausdorff dimension satisfies countable intersection property result matches well known analogous result bounded continued fraction expansions equivalently badly approximable numbers note roth expansions have countably infinite markov partition which leads notion infinite distortion sense markov partitions

Bill Mance  1   ; Jimmy Tseng  2

1 Department of Mathematics Ohio State University Columbus, OH 43210, U.S.A.
2 Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, U.S.A. 
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Bill Mance; Jimmy Tseng. Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists. Acta Arithmetica, Tome 158 (2013) no. 1, pp. 33-47. doi: 10.4064/aa158-1-2

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