Existence of non-preperiodic algebraic points for a rational self-map of infinite order

Ekaterina Amerik

Existence of non-preperiodic algebraic points for a rational self-map of infinite order

Algebraic Geometry 2010-07-12 v1 Dynamical Systems Number Theory

Authors: Ekaterina Amerik

Abstract

Let $X$ be a variety defined over a number field and $f$ be a dominant rational self-map of $X$ of infinite order. We show that $X$ admits many algebraic points which are not preperiodic under $f$ . If $f$ were regular and polarized, this would follow immediately from the theory of canonical heights, but it does not work very well for rational self-maps. We provide an elementary proof following an argument by Bell, Ghioca and Tucker (arxiv:0808.3266).

Keywords

algebraic points preperiodic points rational self-map infinite order number field canonical heights

Cite

@article{arxiv.1007.1635,
  title  = {Existence of non-preperiodic algebraic points for a rational self-map of infinite order},
  author = {Ekaterina Amerik},
  journal= {arXiv preprint arXiv:1007.1635},
  year   = {2010}
}

Comments

6 pages, LaTeX

Related papers

View all related →