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# Mathematical Research Letters

## Volume 19 (2012)

### Number 6

### Canonical heights for plane polynomial maps of small topological degree

Pages: 1207 – 1217

DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n6.a3

#### Authors

#### 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.

#### Keywords

canonical height, dynamical degrees, polynomial mappings, compactifications, arithmetic dynamics

#### 2010 Mathematics Subject Classification

Primary 37P30. Secondary 11G50, 37P15.

Published 18 July 2013