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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… 
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Related topics

Related topics

4 relations
CoefficientDegree of a polynomialJacobian matrix and determinantPolynomial

Papers overview

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2015
2015
Jacobian Conjecture and Nilpotency
For K a field of characteristic 0 and d any integer number greater than or equal to 2, we prove the invertibility of polynomial… 
2014
2014
Involutions and the Jacobian conjecture
The famous Jacobian conjecture asks if an endomorphism $f$ of $K[x,y]$ ($K$ is a characteristic zero field) having a non-zero… 
2013
2013
Lie Subalgebras of vector fields and the Jacobian Conjecture
We study Lie subalgebras $L$ of the vector fields $\mathrm{Vec}^{c}({\mathbb A}^{2})$ of affine 2-space ${\mathbb A}^{2}$ of… 
2012
2012
On the Rational Real Jacobian Conjecture
Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself… 
2008
2008
Plane Jacobian Conjecture for rational polynomials
A non-zero constant Jacobian polynomial maps $F=(P,Q)$ of $\mathbb{C}^2$ is invertible if $P$ and $Q$ are rational polynomials. 
2008
2008
Jacobian trees and their applications
Review
2007
Review
2007
Combinatorial Approaches To The Jacobian Conjecture
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final… 
2004
2004
Note on the Jacobian condition and the non-proper value set
We show that the non-proper value set of a polynomial map (P,Q) : C2 → C2 satisfying the Jacobian condition detD(P,Q) ≡ const 6… 
1996
1996
A proof of the Jacobian conjecture on global asymptotic stability
A classical problem, known as global asymptotic stability Jacobian conjecure or plane Markus-Yamabe conjecture, says that if, the… 
1987
1987
A Note on the Jacobian Conjecture in Two Variables
Let k[x, y] be the polynomial ring over a field le of characteristic zero. If f and g are polynomials in k[x, y] then we denote…