Natural extensions for the Rosen fractions-Reference-Cited by-同舟云学术

Natural extensions for the Rosen fractions

Published:1999-10-15 Issue:3 Volume:352 Page:1277-1298
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Burton Robert,Kraaikamp Cornelis,Schmidt Thomas

Abstract

The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2000-352-03/S0002-9947-99-02442-3/S0002-9947-99-02442-3.pdf

Reference20 articles.

1. Graduate Texts in Mathematics;Beardon, Alan F.,1983

2. Mathematical Centre Tracts;Berbee, Henry C. P.,1979

3. Periodicity and absolute regularity;Berbee, Henry;Israel J. Math.,1986

4. Backward continued fractions and their invariant measures;Gröchenig, Karlheinz;Canad. Math. Bull.,1996

Cited by 24 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Natural extensions and entropy of $ \alpha $-continued fraction expansion maps with odd partial quotients;Discrete and Continuous Dynamical Systems;2023

2. Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics;Ergodic Theory and Dynamical Systems;2022-03-28

3. On the existence of the Legendre constants for some complex continued fraction expansions over imaginary quadratic fields;Journal of Number Theory;2021-09

4. A dependence with complete connections approach to generalized Rényi continued fractions;Acta Mathematica Hungarica;2019-09-04

5. Calculations of the Invariant Measure for Hurwitz Continued Fractions;Experimental Mathematics;2019-06-26