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Dynamical degrees of affine-triangular automorphisms of affine spaces
Published online by Cambridge University Press: 01 October 2021
Abstract
We study the possible dynamical degrees of automorphisms of the affine space 
$\mathbb {A}^n$
. In dimension 
$n=3$
, we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easier case of shift-like automorphisms which can be studied in any dimension. We also prove that each weak Perron number is the dynamical degree of an affine-triangular automorphism of the affine space 
$\mathbb {A}^n$
for some n, and we give the best possible n for quadratic integers, which is either 
$3$
or 
$4$
.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
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