Journal of the Mathematical Society of Japan

Natural extensions for α-Rosen continued fractions

Cornelis KRAAIKAMP, Thomas A. SCHMIDT, and Ionica SMEETS

Full-text: Open access

Abstract

We give natural extensions for the α-Rosen continued fractions of Dajani et al. for a set of small α values by appropriately adding and deleting rectangles from the region of the natural extension for the standard Rosen fractions. It follows that the underlying maps have equal entropy.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 2 (2010), 649-671.

Dates
First available in Project Euclid: 7 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1273236716

Digital Object Identifier
doi:10.2969/jmsj/06220649

Mathematical Reviews number (MathSciNet)
MR2662856

Zentralblatt MATH identifier
1209.11078

Subjects
Primary: 11K50: Metric theory of continued fractions [See also 11A55, 11J70]
Secondary: 37A45: Relations with number theory and harmonic analysis [See also 11Kxx] 37A35: Entropy and other invariants, isomorphism, classification

Keywords
Rosen fractions natural extensions entropy

Citation

KRAAIKAMP, Cornelis; SCHMIDT, Thomas A.; SMEETS, Ionica. Natural extensions for α-Rosen continued fractions. J. Math. Soc. Japan 62 (2010), no. 2, 649--671. doi:10.2969/jmsj/06220649. https://projecteuclid.org/euclid.jmsj/1273236716


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