References
- Abrams, A. (2016). Bijectivity and trapping regions for complex continued fraction transformation. Master’s Paper. Pennsylvania State University, arXiv:1608.06351.
- Adler, R., Flatto L. (1982). Cross section maps for geodesic flows, I (The modular surface). In: Katok, A., ed. Progress in Mathematics. Boston, MA: Birkhäuser, pp. 103–161.
- Adler, R., Flatto, L. (1984). Cross section map for geodesic flow on the modular surface. Contemp. Math., 26: 9–23.
- Artin, E. (1965). Ein mechanisches system mit quasiergodischen bahnen. Collected Papers. Reading, MA: Addison Wesley, pp. 499–501. (German).
- Dani, S. G., Nogueira, A. (2014). Continued Fractions for Complex Numbers and Values of Binary Quadratic Forms. Providence, RI: Transactions of the American Mathematical Society.
- Ei, H., Ito, S., Nakada, H., Natsui, R. (2019). On the construction of the natural extension of the Hurwitz complex continued fraction map. Monat. Math. 188: 37–86. doi:10.1007/s00605-018-1229-0
- Hensley, D. (2006). Continued Fractions. Singapore: World Scientific Publishing Co. Pte. Ltd.
- Hurwitz, A. (1887). Über die entwicklung complexer größen in kettenbruc¨he. Acta Math. 11: 187–200 (German). doi:10.1007/BF02612324
- Hurwitz, J. (1902). Über die reduction der binären quadratischen formen mit complexen coefficienten und variabeln. Acta Math. 25: 231–290 (German) doi:10.1007/BF02419027
- Katok, S., Ugarcovici, I. (2005). Arithmetic coding of geodesics on the modular surface via continued fractions. Centrum Wiskunde Info. Amsterdam. 135: 59–77.
- Katok, S., Ugarcovici, I. (2010), Structure of attractors for (a, b)-continued fraction transformations. J. Mod. Dynam. 4: 637–691. doi:10.3934/jmd.2010.4.637
- Katok, S., Ugarcovici, I. (2012). Applications of (a, b)-continued fraction transformations. Ergod. Theory Dynam. Syst. 32: 755–777.
- Nakada, H., Ito, S., Tanaka, S. (1977). On the invariant measure for the transformations associated to with some real continued fractions. Kieo Eng. Rep. 30: 159–175.
- Oswald, N. (2014). Hurwitz’s complex continued fractions: a historical approach and modern perspectives. Doctoral Thesis, Julius-Maximilians-Universität Würzburg, Würzburg.
- Series, C. (1981). Symbolic dynamics for geodesic flows. Acta Math. 146:103–128. doi:10.1007/BF02392459
- Series, C. (1985). The modular surface and continued fractions. J. Lond. Math. Soc. 31: 69–80. doi:10.1112/jlms/s2-31.1.69
- Tanaka, S. (1985). A complex continued fraction transformation and its ergodic properties. Tokyo J. Math. 8: 191–214. doi:10.3836/tjm/1270151579