Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists

• Autorzy: Bill Mance , Jimmy Tseng
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 11K50: Metric theory of continued fractions
• 11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 1
• Strony: 33-47

Daty

wydano

2013

Twórcy

autor

Bill Mance

• Department of Mathematics, Ohio State University, Columbus, OH 43210, U.S.A.

autor

Jimmy Tseng

• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/aa158-1-2