an:05885281
Zbl 1222.37012
Smillie, John; Ulcigrai, Corinna
Geodesic flow on the Teichm??ller disk of the regular octagon cutting sequences and octagon continued fractions maps
EN
Kolyada, Sergiy (ed.) et al., Dynamical numbers. Interplay between dynamical systems and number theory. A special program, May 1--July 31, 2009. International conference, MPI, Bonn, Germany, July 20--24, 2009. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4958-3). Contemporary Mathematics 532, 29-65 (2010).
2010
a
37B10 11J70 37E35
coding trajectories; Teichm??ller disk; octagon continued fraction maps
In an earlier paper the authors investigated the problem of characterizing symbol sequences that arise in coding constant slope trajectories on the regular octagon with opposite sides identified. They developed a continued fraction algorithm and a related Farey map. In the present paper they continue that work by giving ``a geometric interpretation of the renormalization algorithm and of the continued fraction map \dots introduced [there] to give a characterization of symbolic sequences'' mentioned above. They ``interpret this algorithm as renormalization on the Teichm??ller disk of the octagon and explain the relation with Teichm??ller geodesic flow'', and use it to analyze further the continued fraction map.
For the entire collection see [Zbl 1205.00087].
Douglas S. Shafer (Charlotte)