$A_2$-continued fraction representation of real numbers and its geometry

• Datum: 2009
• Hauptverfasser: Dmytrenko, S. O., Kyurchev, D. V., Pratsiovytyi, M. V., Дмитренко, С. O., Кюрчев, Д. В., Працьовитий, М. В.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2009
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3033
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study the geometry of representations of numbers by continued fractions whose elements belong to the set $A_2 = {α_1, α_2}$ ($A_2$-continued fraction representation). It is shown that, for $α_1 α_2 ≤ 1/2$, every point of a certain segment admits an $A_2$-continued fraction representation. Moreove...