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Dynamical Belyi Maps

  • Jacqueline Anderson
  • Irene I. Bouw
  • Ozlem Ejder
  • Neslihan Girgin
  • Valentijn Karemaker
  • Michelle ManesEmail author
Conference paper
Part of the Association for Women in Mathematics Series book series (AWMS, volume 11)

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.

Keywords

Arithmetic dynamics Conservative rational maps Reduction 

Notes

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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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Jacqueline Anderson
    • 1
  • Irene I. Bouw
    • 2
  • Ozlem Ejder
    • 3
  • Neslihan Girgin
    • 4
  • Valentijn Karemaker
    • 5
  • Michelle Manes
    • 6
    Email author
  1. 1.Bridgewater State UniversityBridgewaterUSA
  2. 2.University of UlmUlmGermany
  3. 3.Colorado State UniversityFort CollinsUSA
  4. 4.Boǧaziçi UniversityIstanbulTurkey
  5. 5.University of PennsylvaniaPhiladelphiaUSA
  6. 6.University of HawaiiHonoluluUSA

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