Farey maps, Diophantine approximation and Bruhat-Tits tree

Dong Han Kim, Seonhee Lim, Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 map, 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.

Original languageEnglish
Pages (from-to)14-32
Number of pages19
JournalFinite Fields and Their Applications
Volume30
DOIs
Publication statusPublished - 2014

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Diophantine Approximation
Gauss Map
Geodesic Flow
Ergodic Measure
Formal Power Series
Continued fraction
Invariant Measure
Galois field
Continue
Coding
Coefficient

Keywords

  • Artin map
  • Bruhat-Tits tree
  • Continued fraction
  • Diophantine approximation
  • Farey map
  • Field of formal Laurent series
  • Intermediate convergents

ASJC Scopus subject areas

  • Applied Mathematics
  • Algebra and Number Theory
  • Theoretical Computer Science
  • Engineering(all)

Cite this

Farey maps, Diophantine approximation and Bruhat-Tits tree. / Kim, Dong Han; Lim, Seonhee; Nakada, Hitoshi; Natsui, Rie.

In: Finite Fields and Their Applications, Vol. 30, 2014, p. 14-32.

Research output: Contribution to journalArticle

Kim, Dong Han ; Lim, Seonhee ; Nakada, Hitoshi ; Natsui, Rie. / Farey maps, Diophantine approximation and Bruhat-Tits tree. In: Finite Fields and Their Applications. 2014 ; Vol. 30. pp. 14-32.
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