Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps

@article{Smillie2010GeodesicFO,
title={Geodesic flow on the Teichmueller disk of the regular octagon, cutting sequences and octagon continued fractions maps},
author={J. Smillie and C. Ulcigrai},
journal={arXiv: Dynamical Systems},
year={2010}
}

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… Expand