Canonical Height Functions on the Affine Plane Associated with Polynomial Automorphisms

@inproceedings{Kawaguchi2006CanonicalHF,
  title={Canonical Height Functions on the Affine Plane Associated with Polynomial Automorphisms},
  author={Shu Kawaguchi},
  year={2006}
}
Let f : A → A be a polynomial automorphism of dynamical degree δ ≥ 2 over a number field K. (This is equivalent to say that f is a polynomial automorphism that is not triangularizable.) Then we construct canonical height functions defined on A(K) associated with f . These functions satisfy the Northcott finiteness property, and an Kvalued point on A(K) is f -periodic if and only if its height is zero. As an application of canonical height functions, we give an estimate on the number of points… CONTINUE READING