Year: 2026
Type: article
Abstract: This paper studies the properness of polynomial selfmaps $$F:\mathbb {R}^m \rightarrow \mathbb {R}^m$$ F : R m → R m or $$F:\mathbb {C}^m\rightarrow \mathbb {C}^m$$ F : C m → C m . By results of Druzkowski, this question is reduced to that of properness of maps of the following special form, which we call identity plus linear powers. For two vectors $$x,y\in \mathbb {R}^m$$ x , y ∈ R m , we use the notation $$x *y =(x_1y_1,\ldots ,x_my_m)$$ x ∗ y = ( x 1 y 1 , … , x m y m ) , and if $$x=y$$ x = y we also use the notation $$x^2=x*x$$ x 2 = x ∗ x and by induction $$x^k=x*(x^{k-1})$$ x k = x ∗ ( x k - 1 ) . We use $$\langle ,\,\rangle $$ ⟨ , ⟩ for the usual inner product on $$\mathbb {R}^m$$ R m . For A an $$m\times m$$ m × m <
Source: Vietnam Journal of Mathematics
Author: Tuyen Trung Truong
Institution: University of Oslo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Award: G4559354364
OpenAlex ID: W7141984277