Abstract
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.
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Acknowledgements
This project began at the Women in Numbers Europe 2 conference at the Lorentz Center. We thank the Lorentz Center for providing excellent working conditions, and we thank the Association for Women in Mathematics for supporting WIN-E2 and other research collaboration conferences for women through their NSF ADVANCE grant. We also thank the referee for numerous helpful comments, all of which greatly improved the paper.
MM partially supported by NSF-HRD 1500481 (AWM ADVANCE grant) and by the Simons Foundation grant #359721.
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Anderson, J., Bouw, I.I., Ejder, O., Girgin, N., Karemaker, V., Manes, M. (2018). Dynamical Belyi Maps. In: Bouw, I., Ozman, E., Johnson-Leung, J., Newton, R. (eds) Women in Numbers Europe II. Association for Women in Mathematics Series, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-74998-3_5
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DOI: https://doi.org/10.1007/978-3-319-74998-3_5
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