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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

Semantic Scholar uses AI to extract papers important to this topic.
2017
2017
Some remarks to the Jacobian Conjecture
This work is related to the Jacobian Conjecture. It contains the formulas concerning algebraic dependence of the polynomial… 
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… 
2011
2011
A characterization of Keller maps
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. 
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… 
Review
1999
Review
1999
Monodromy, differential equations and the Jacobian conjecture
We study certain problems on polynomial mappings related to the Jacobian conjecture. 0. Introduction. Let F : C → C, n > 1, be a… 
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… 
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