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Farey maps, Diophantine approximation and Bruhat-Tits treeopen access
- Authors
- Kim, Dong Han; Lim, Seonhee; Nakada, Hitoshi; Natsui, Rie
- Issue Date
- Nov-2014
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Farey map; Field of formal Laurent series; Intermediate convergents; Diophantine approximation; Bruhat-Tits tree; Artin map; Continued fraction
- Citation
- FINITE FIELDS AND THEIR APPLICATIONS, v.30, pp 14 - 32
- Pages
- 19
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- FINITE FIELDS AND THEIR APPLICATIONS
- Volume
- 30
- Start Page
- 14
- End Page
- 32
- ISSN
- 1071-5797
1090-2465
- Abstract
- Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents via the symbolic coding of the geodesic flow of the continued fraction algorithm for formal power series with coefficients in a finite field, we continue the study of the Gauss map via Farey maps to contain all the intermediate convergents. We define the geometric Farey nap, which is given by time-one map of the geodesic flow. We also define algebraic Farey maps, better suited for arithmetic properties, which produce all the intermediate convergents. Then we obtain the ergodic invariant measures for the Farey maps and the convergent speed. (C) 2014 Elsevier Inc. All rights reserved.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)