Results 221 to 230 of about 25,672 (245)

The Jacobian conjecture. I

2012
See the following review.
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The Jacobian Conjecture and Nilpotent Maps

Journal of Mathematical Sciences, 2001
The paper is devoted to the next equivalent condition to the Jacobian conjecture. A polynomial mapping \(N=(N_1,\dots ,N_n):\mathbb C^n \to \mathbb C^n\) is called nilpotent iff its jacobian matrix is nilpotent, i.e. \(\Biggl(\frac{\partial N_i}{\partial X_j}\Biggr)^m=0\).
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Towards the Jacobian Conjecture

Algebra Colloquium
We first show that if there is a counterexample to the two-dimensional Jacobian conjecture, then there exists a nonempty closed smooth affine surface in [Formula: see text] satisfying various properties. Next, we conjecture that such a surface does not exist.
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Two notes on the Jacobian Conjecture

Archiv der Mathematik, 1987
Let K be a field of characteristic zero, let \(F=(F_ 1,...,F_ n)\) denote the endomorphism of \(K[X_ 1,...,X_ n]\) defined by \(X_ i\mapsto F_ i\), where \(F_ 1,...,F_ n\in K[X_ 1,...,X_ n]\), and let \(J(F)=(\partial F_ i/\partial X_ j)\) denote the Jacobian matrix of this endomorphism.
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Jacobian Conjecture as a Problem on Integral Points on Affine Curves

Vietnam Journal of Mathematics, 2021
Van Chau Nguyen
exaly  

A Generalization of the Poincaré Compactification and the Real Jacobian Conjecture

Journal of Dynamics and Differential Equations, 2022
Claudia Valls
exaly  

Some thoughts on the Jacobian conjecture. I

2008
A pair \(f,g\in k[X,Y]\) is called a Jacobian pair if \(det(Jac(f,g))\in k^*\). The author reported on p. 181 of \textit{S. S. Abhyankar} [Proc. Indian Acad. Sci., Math. Sci. 104, No. 3, 515--542 (1994; Zbl 0812.13013)] the following: if \(f,g\) is a Jacobian pair and \noindent[1] either: \(H\leq 2\) (two characteristic pair case) \noindent[2] or: \(H ...
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On the shape of possible counterexamples to the Jacobian Conjecture

Journal of Algebra, 2017
Christian Valqui, Juan J Guccione
exaly  

Jacobian Conjecture

1995
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A connection between isochronous Hamiltonian centres and the Jacobian Conjecture

Nonlinear Analysis: Theory, Methods & Applications, 1998
Marco Sabatini
exaly