Attracting cycles in $p$-adic dynamics and height bounds for postcritically finite maps

  title={Attracting cycles in \$p\$-adic dynamics and height bounds for postcritically finite maps},
  author={Robert L. Benedetto and Patrick Ingram and Rafe Jones and Alon Y. Levy},
  journal={Duke Mathematical Journal},
A rational function of degree at least two with coefficients in an algebraically closed field is post-critically finite (PCF) if all of its critical points have finite forward orbit under iteration. We show that the collection of PCF rational functions is a set of bounded height in the moduli space of rational functions over the complex numbers, once the well-understood family known as flexible Lattes maps is excluded. As a consequence, there are only finitely many conjugacy classes of non… 

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