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.
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