Dynamical Belyi maps. (English) Zbl 1405.37093
Bouw, Irene I. (ed.) et al., Women in numbers Europe II. Contributions to number theory and arithmetic geometry. Proceedings of the 2nd conference, Leiden, The Netherlands, September 26–30, 2016. Cham: Springer (ISBN 978-3-319-74997-6/hbk; 978-3-319-74998-3/ebook). Association for Women in Mathematics Series 11, 57-82 (2018).
Summary: We study the dynamical properties of a large class of rational maps with exactly three ramification points. By constructing families of such maps, we obtain \(\mathcal O(d^2)\) conservative maps of fixed degree \(d\) defined over \(\mathbb Q\); this answers a question of Silverman. Rather precise results on the reduction of these maps yield strong information on their \(\mathbb Q\)-dynamics.
For the entire collection see [Zbl 1398.11005].
For the entire collection see [Zbl 1398.11005].
MSC:
| 37P05 | Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps |
| 11G32 | Arithmetic aspects of dessins d’enfants, Belyĭ theory |
| 14G40 | Arithmetic varieties and schemes; Arakelov theory; heights |
