Farey Maps, Diophantine Approximation and Bruhat-Tits tree
Farey Maps, Diophantine Approximation and Bruhat-Tits tree
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Farey 地图、丢番图近似和 Bruhat-Tits 树
DOI：
10.1016/j.ffa.2014.05.007
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发表时间：
2014
影响因子：
1
通讯作者：
and Rie Natsui
中科院分区：
文献类型：
--
作者：
Dong Han Kim;Seonhee Lim;Hitoshi Nakada;and Rie Natsui
本文在Broise-Alamichel和Paulin关于有限域上系数形式幂级数连分式算法的测地流符号编码的主收敛对应的Gauss映射的基础上，继续研究了包含所有中间收敛的Gauss映射的Farey映射.我们定义了几何Farey映射，它是由测地线流的时一映射给出的。我们还定义了代数Farey地图，更适合于算术属性，产生所有的中间convertability。得到了Farey映射的遍历不变测度和收敛速度。
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.