Canonical heights for plane polynomial maps of small topological degree

2012/02/01 by Jonsson, Mattias, Wulcan, Elizabeth · 1 citation
#37P15 (Secondary) #37P30 (Primary) 11G50 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1202.0203

Abstract

We study canonical heights for plane polynomial mappings of small topological degree. In particular, we prove that for points of canonical height zero, the arithmetic degree is bounded by the topological degree and hence strictly smaller than the first dynamical degree. The proof uses the existence, proved by Favre and the first author, of certain compactifications of the plane adapted to the dynamics.

Cited by

• Rational self-maps of projective surfaces with a regular iterate

Related

• A lower bound on the canonical height for polynomials
• Canonical height functions on the affine plane associated with polynomial automorphisms
• Lower Bounds for the Canonical Height of a Unicritical Polynomial and Capacity
• A Bogomolov property for the canonical height of maps with superattracting periodic points
• On lower bounds for canonical heights of the map ϕ(X,Y)=(Y,X+Y^D+b)