English

On the complex dynamics of birational surface maps defined over number fields

Dynamical Systems 2015-12-09 v2 Complex Variables Number Theory

Abstract

We show that any birational selfmap of a complex projective surface that has dynamical degree greater than one and is defined over a number field automatically satisfies the Bedford-Diller energy condition after a suitable birational conjugacy. As a consequence, the complex dynamics of the map is well-behaved. We also show that there is a well-defined canonical height function.

Keywords

Cite

@article{arxiv.1505.03559,
  title  = {On the complex dynamics of birational surface maps defined over number fields},
  author = {Mattias Jonsson and Paul Reschke},
  journal= {arXiv preprint arXiv:1505.03559},
  year   = {2015}
}

Comments

Added simplified argument for algebraically stable maps on the projective plane. To appear in Crelle's Journal. 19 pages

R2 v1 2026-06-22T09:33:52.450Z