Dynamical degrees of affine-triangular automorphisms in dimension four
Algebraic Geometry
2025-09-19 v1 Dynamical Systems
Abstract
In this paper, let k be the affine n-space over an arbitrary field k. We show that dynamical degrees of affine-triangular automorphisms in dimension 4 are algebraic integers of degree not larger than 4. As a consequence, if char(k) is not equal to 2, then dynamical degrees of quadratic automorphisms in dimension 4 are algebraic integers of degree not larger than 4. We also explore some results in higher dimensions. These results partially give the affirmative answer to the Conjecture in DF21
Cite
@article{arxiv.2509.14584,
title = {Dynamical degrees of affine-triangular automorphisms in dimension four},
author = {Enbo Shao and Xiaosong Sun},
journal= {arXiv preprint arXiv:2509.14584},
year = {2025}
}