Results 11 to 20 of about 25,672 (245)
The Jacobian Conjecture and Injectivity Conditions [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2018 14 pages; Submitted to a ...
Saminathan Ponnusamy, Victor V. Starkov
openaire +5 more sources
Journal of Pure and Applied Algebra, 1990 Let F: \({\mathbb{C}}^ 2\to {\mathbb{C}}^ 2\) be a map defined by the polynomials \(F_ 1,F_ 2\in {\mathbb{C}}[X_ 1,X_ 2]\), \({\mathbb{C}}\) the complex numbers. The two-dimensional Jacobian conjecture states that F is invertible (and the inverse is a polynomial map) if and only if \(\det (\partial F_ i/\partial X_ j)\in {\mathbb{C}}^*\).
David A Jorgensen
openaire +4 more sources
Irreducibility properties of Keller maps [PDF]
, 2016 Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials.
de Bondt, Michiel, Yan, Dan
core +2 more sources
The Gaussian Moments Conjecture and the Jacobian Conjecture [PDF]
Israel Journal of Mathematics, 2017 We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing Conjecture .
Derksen, H. +2 more
openaire +5 more sources
Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras
Mathematics, 2022 This paper surveys results concerning the quantization approach to the Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of the paper and its motivations.
Wenchao Zhang +5 more
doaj +1 more source
On the Jacobian Conjecture [PDF]
Proceedings of the American Mathematical Society, 1993 We show that the Jacobian conjecture can be reduced to a weaker conjecture in which all fibers of coordinate functions are irreducible.
openaire +2 more sources
The Jacobian conjecture for symmetric Jacobian matrices
Journal of Pure and Applied Algebra, 2004 Let \(F = (F_1,\ldots,F_n) : \mathbb C^n \longrightarrow \mathbb C^n\) be a polynomial map and \(J(F) = (\partial F_i/\partial x_j)\) the Jacobian matrix of \(F\). The Jacobian conjecture asserts that \(F\) is invertible if det\((J(F)) \in \mathbb C^*\).
van den Essen, Arno, Washburn, Sherwood
openaire +1 more source
THE JACOBIAN CONJECTURE: STRUCTURE OF KELLER MAPPINGS
Проблемы анализа, 2019 The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of the polynomial mapping f : R n → R n (C n → C n ) under the assumption that Jf ≡ const 6= 0.
V. V. Starkov
doaj +1 more source
STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE
Проблемы анализа, 2017 A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian J_ƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case n = 2,
V. V. Starkov
doaj +1 more source
Analytic Automorphisms and Transitivity of Analytic Mappings
Mathematics, 2020 In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators.
Zoriana Novosad, Andriy Zagorodnyuk
doaj +1 more source