Journal of the Mathematical Society of Japan

Natural extensions for α-Rosen continued fractions

Cornelis KRAAIKAMP, Thomas A. SCHMIDT, and Ionica SMEETS

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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

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

First available in Project Euclid: 7 May 2010

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Zentralblatt MATH identifier

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

Rosen fractions natural extensions entropy


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.

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