Equivariant Polynomial Automorphisms Of Θ-Representations

1998 ◽  
Vol 50 (2) ◽  
pp. 378-400
Author(s):  
Alexandre Kurth

AbstractWe show that every equivariant polynomial automorphism of a Θ- representation and of the reduction of an irreducible Θ-representation is a multiple of the identity.

2019 ◽  
Vol 29 (05) ◽  
pp. 803-825 ◽  
Author(s):  
Eric Edo ◽  
Drew Lewis

A polynomial automorphism of [Formula: see text] over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms of [Formula: see text], including nonaffine [Formula: see text]-triangular automorphisms, are co-tame. Of particular interest, if [Formula: see text], we show that the statement “Every [Formula: see text]-triangular automorphism is either affine or co-tame” is true if and only if [Formula: see text]; this improves upon positive results of Bodnarchuk (for [Formula: see text], in any dimension [Formula: see text]) and negative results of the authors (for [Formula: see text], [Formula: see text]). The main technical tool we introduce is a class of maps we term translation degenerate automorphisms; we show that all of these are either affine or co-tame, a result that may be of independent interest in the further study of co-tame automorphisms.


Astérisque ◽  
2020 ◽  
Vol 415 ◽  
pp. 35-43
Author(s):  
Romain DUJARDIN

2003 ◽  
Vol 68 (1) ◽  
pp. 73-79
Author(s):  
Takis Sakkalis

This note relates polynomial remainders with polynomial automorphisms of the plane. It also formulates a conjecture, equivalent to the famous Jacobian Conjecture. The latter provides an algorithm for checking when a polynomial map is an automorphism. In addition, a criterion is presented for a real polynomial map to be bijective.


1997 ◽  
Vol 197 (2) ◽  
pp. 546-558 ◽  
Author(s):  
Vladimir Shpilrain ◽  
Jie-Tai Yu

2016 ◽  
Vol 8 (1) ◽  
pp. 127-133 ◽  
Author(s):  
Z.G. Mozhyrovska

In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular, we show that an "symmetric translation" operator is hypercyclic on a Frechet algebra of symmetric entire functions on $\ell_p$ which are bounded on bounded subsets.


2009 ◽  
Vol 37 (10) ◽  
pp. 3388-3400
Author(s):  
Gérard Endimioni

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