On Minkowski type question mark functions associated with even or odd continued fractions

On Minkowski type question mark functions associated with even or odd continued fractions

We study analogues of Minkowski’s question mark function ?( x ) related to continued fractions with even or with odd partial quotients. We prove that these functions are Hölder continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.

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Veröffentlicht in:Monatshefte für Mathematik 2018-09, Vol.187 (1), p.35-57
Hauptverfasser: Boca, Florin P., Linden, Christopher
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
Mathematics
Mathematics and Statistics
Quotients
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Beschreibung
Zusammenfassung:We study analogues of Minkowski’s question mark function ?( x ) related to continued fractions with even or with odd partial quotients. We prove that these functions are Hölder continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-018-1205-8