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arXiv · 2509.14584

Dynamical degrees of affine-triangular automorphisms in dimension four

Enbo Shao·Xiaosong Sun
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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

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Enbo Shao, Xiaosong Sun. 2025-09-18. Dynamical degrees of affine-triangular automorphisms in dimension four. https://arxiv.org/abs/2509.14584

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