Jacobian conjecture

Known as: Jacobian problem, Keller's problem, Smale's sixteenth problem 
In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich… (More)
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2009
2009
The Jacobian Conjecture is the following : If φ ∈ Endk(Ank ) with a field k of characteristic zero is unramified, then φ is an… (More)
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2008
2008
A non-zero constant Jacobian polynomial map F = (P, Q) : C → C has a polynomial inverse if the component P is a simple polynomial… (More)
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2004
2004
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero in… (More)
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2004
2004
Let z = (z1, · · · , zn) and let ∆ = ∑n i=1 ∂2 ∂z2 i be the Laplace operator. The main goal of the paper is to show that the well… (More)
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2004
2004
  • Ludwik M. Drużkowski
  • 2004
It is sufficient to consider in the Jacobian Conjecture (for every n > 1) only polynomial mappings of cubic linear form F (x) = x… (More)
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2004
2004
Let K[x, y] be the algebra of two-variable polynomials over a field K. A polynomial p = p(x, y) is called a test polynomial for… (More)
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2001
2001
New combinatorial properties of Catalan trees are established and used to prove a number of algebraic results related to the… (More)
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Review
2000
Review
2000
In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent… (More)
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1998
1998
We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a… (More)
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Highly Cited
1982
Highly Cited
1982
Introduction I. The Jacobian Conjecture 1. Statement of the Jacobian Problem; first observations 2. Some history of the Jacobian… (More)
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