正八边形Teichmueller圆盘上的测地流、切割序列和八边形连分数映射
Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps
摘要：
在本文中，我们给出了一个几何解释的重整化算法和连分数映射，我们介绍了arxiv：0905.0871中给出的线性流的符号序列的特征，在正八边形。我们将此算法解释为八边形Teichmueller圆盘上的重整化，并解释了与Teichmueller测地流的关系。这种联系类似于Sturmian序列、连分数和模曲面上的测地流之间的经典关系。利用这种联系，我们构造了连分数映射的自然扩张和不变测度。定义了具有有限不变测度的连分数映射的加速度。
英文摘要：
In this paper we give a geometric interpretation of the renormalization algorithm and of the continued fraction map that we introduced in arxiv:0905.0871 to give a characterization of symbolic sequences for linear flows in the regular octagon. We interpret this algorithm as renormalization on the Teichmueller disk of the octagon and explain the relation with Teichmueller geodesic flow. This connection is analogous to the classical relation between Sturmian sequences, continued fractions and geodesic flow on the modular surface. We use this connection to construct the natural extension and the invariant measure for the continued fraction map. We also define an acceleration of the continued fraction map which has a finite invariant measure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
