Canonical height functions for affine plane automorphisms

@article{Kawaguchi2006CanonicalHF,
  title={Canonical height functions for affine plane automorphisms},
  author={Shu Kawaguchi},
  journal={Mathematische Annalen},
  year={2006},
  volume={335},
  pages={285-310}
}
  • Shu Kawaguchi
  • Published 7 April 2006
  • Mathematics
  • Mathematische Annalen
Let be a polynomial automorphism of dynamical degree δ≥2 over a number field K. We construct height functions defined on that transform well relative to f, which we call canonical height functions for f. These functions satisfy the Northcott finiteness property, and a -valued point on is f-periodic if and only if its height is zero. As an application, we give an estimate on the number of points with bounded height in an infinite f-orbit. 

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