## Journal of the Mathematical Society of Japan

### Natural extensions for α-Rosen continued fractions

#### 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

https://projecteuclid.org/euclid.jmsj/1273236716

Digital Object Identifier
doi:10.2969/jmsj/06220649

Mathematical Reviews number (MathSciNet)
MR2662856

Zentralblatt MATH identifier
1209.11078

#### 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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