1 results
Dynamical degrees of affine-triangular automorphisms of affine spaces
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 12 / December 2022
- Published online by Cambridge University Press:
- 01 October 2021, pp. 3551-3592
- Print publication:
- December 2022
-
- Article
- Export citation
-
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 
$4$
.
