Dynamical degrees of affine-triangular automorphisms of affine spaces
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...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2022-12, Vol.42 (12), p.3551-3592 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | BLANC, JÉRÉMY VAN SANTEN, IMMANUEL |
| description | 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
$4$
. |
| doi_str_mv | 10.1017/etds.2021.90 |
| format | Article |
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$\mathbb {A}^n$
. 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
$4$
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$\mathbb {A}^n$
. 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
$4$
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$\mathbb {A}^n$
. 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
$4$
.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/etds.2021.90</doi><tpages>42</tpages></addata></record> |
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| identifier | ISSN: 0143-3857 |
| ispartof | Ergodic theory and dynamical systems, 2022-12, Vol.42 (12), p.3551-3592 |
| issn | 0143-3857 1469-4417 |
| language | eng |
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| source | Cambridge Journals |
| subjects | Algebra Automorphisms Original Article |
| title | Dynamical degrees of affine-triangular automorphisms of affine spaces |
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