Dynamical degrees of affine-triangular automorphisms of affine spaces
| Autor: | Jérémy Blanc, Immanuel van Santen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Degree (graph theory) Applied Mathematics General Mathematics Dimension (graph theory) Composition (combinatorics) Automorphism Mathematics::Group Theory Mathematics - Algebraic Geometry Quadratic integer Affine space Perron number Affine transformation Mathematics - Dynamical Systems 14R10 37F10 Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. 42:3551-3592 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2021.90 |
| Popis: | 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 somen, and we give the best possiblenfor quadratic integers, which is either$3$or$4$. |
| Databáze: | OpenAIRE |
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