Related papers: On the Jacobian conjecture
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
We prove that the Jacobian conjecture is false if and only if there exists a solution to a certain system of polynomial equations. We analyse the solution set of this system. In particular we prove that it is zero dimensional.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.
We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.
The two dimensional Jacobian Conjecture says that a morphism $f:\mathbb{C}[x,y]\to \mathbb{C}[x,y]$ having an invertible Jacobian, is invertible. We show that a morphism $f$ having an invertible Jacobian is invertible, in each of the…
We investigate the 2-dimensional jacobian conjecture via Klein's program.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.
The Jacobian Conjecture states that any locally invertible polynomial system in C^n is globally invertible with polynomial inverse. C. W. Bass et al. (1982) proved a reduction theorem stating that the conjecture is true for any degree of…
This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…
We prove the Jacobian Conjecture for the space of all the inner functions in the unit disc.
We construct a non-proper set of two variables polynomial maps and study the nowhere vanishing Jacobian condition of the Jacobian conjecture for this set. We obtain some classes of polynomial maps satisfying the 2-dimensional Jacobian…
The present paper is devoted to investigating the two-dimensional real Jacobian conjecture. This conjecture claims that if $F=\left(f,g\right):\mathbb{R}^2\rightarrow \mathbb{R}^2$ is a polynomial map with $\det DF\left(x,y\right)\ne0$ for…
For any integer $d \geq 1$, we verify the Jacobian Conjecture for a $d$-linear map in two variables. We prove that almost all the coefficients of the formal inverse are in the ideal specified by the Jacobian condition. We find expressions…
The two-dimensional Jacobian Conjecture says that a $\mathbb{C}$-algebra endomorphism $F:\mathbb{C}[x,y] \to \mathbb{C}[x,y]$ that has an invertible Jacobian is an automorphism. We show that if a $\mathbb{C}$-algebra endomorphism…
Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…
Jacobian conjecture states that if $F:\ \mathbb C^n(\mathbb R^n)\rightarrow \mathbb C^n(\mathbb R^n)$ is a polynomial map such that the Jacobian of $F$ is a nonzero constant, then $F$ is injective. This conjecture is still open for all…
The direct or algorithmic approach for the Jacobian problem, consisting of the direct construction of the inverse polynomials is proposed. The so called principle and derived Jacobi conditions are proposed and discussed. The algorithmic…