Related papers: A new method in the Jacobian Conjecture
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
We show that the Jacobian conjecture of the two dimensional case is true.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We investigate the 2-dimensional jacobian conjecture via Klein's program.
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 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.
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
We present several versions of the Jacobian Conjecture in positive characteristic each of which if true would imply the Jacobian conjecture in characteristic 0. We test these characteristic p versions of the conjecture against several…
Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.
We present some motivations and discuss various aspects of an approach to the Jacobian Conjecture in terms of irreducible elements and square-free elements.
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 algebras are introduced and their various properties are studied.
The Jacobian conjecture is an old unsolved problem in mathematics, which has been unsuccessfully attacked from many different angles. We add here another point of view pertaining to the so called formal inverse approach, that of…
The paper titled "Cremona problem in dimension 2" by W. Bartenwerfer presented a flawed attempt at proving the Jacobian Conjecture. Our aim is to provide a thorough analysis of the author's approach, highlighting the errors that were made…
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…
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…
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…
We introduce a new method for studying the Baum-Connes conjecture, which we call the direct splitting method. The method can simplify and clarify proofs of some of the known cases of the conjecture. In a separate paper, with J. Brodzki, E.…