- Tytuł:
- The Jacobian Conjecture in case of "non-negative coefficients"
- Autorzy:
- Drużkowski, Ludwik
- Powiązania:
- https://bibliotekanauki.pl/articles/1294772.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
polynomial automorphisms
nilpotent matrix
Jacobian Conjecture - Opis:
-
It is known that it is sufficient to consider in the Jacobian Conjecture only polynomial mappings of the form
$F(x₁,...,x_n) = x - H(x) := (x₁ - H₁(x₁,...,x_n),...,x_n - H_n(x₁,...,x_n))$,
where $H_j$ are homogeneous polynomials of degree 3 with real coefficients (or $H_j = 0$), j = 1,...,n and H'(x) is a nilpotent matrix for each $x = (x₁,...,x_n) ∈ ℝ^n$.
We give another proof of Yu's theorem that in the case of non-negative coefficients of H the mapping F is a polynomial automorphism, and we moreover prove that in that case $deg F^{-1} ≤ (deg F)^{ind F - 1}$, where $ind F := max{ind H'(x): x ∈ ℝ^n}$. Note that the above inequality is not true when the coefficients of H are arbitrary real numbers; cf. [E3]. - Źródło:
-
Annales Polonici Mathematici; 1997, 66, 1; 67-75
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł