A reduction of the Jacobian Conjecture to the symmetric case

Bondt, Michiel de; Essen, Arno van den

doi:10.1090/s0002-9939-05-07570-2

Cited by 42 publications

(30 citation statements)

References 12 publications

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“…That is why the above theorem is considered to be due to Meng. The case that J H is nilpotent of corollary 1.4 below was proved in [2].…”

Section: H Rmentioning

confidence: 96%

Symmetric Jacobians

Bondt

2014

Open Mathematics

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Abstract:This article is about polynomial maps with a certain symmetry and/or antisymmetry in their Jacobians, and whether the Jacobian Conjecture is satisfied for such maps, or whether it is sufficient to prove the Jacobian Conjecture for such maps. For instance, we show that it suffices to prove the Jacobian conjecture for polynomial maps + H over C such that JH satisfies all symmetries of the square, where H is homogeneous of arbitrary degree ≥ 3. MSC:14R15, 14R10, 15B99, 15B57, 20F55

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“…That is why the above theorem is considered to be due to Meng. The case that J H is nilpotent of corollary 1.4 below was proved in [2].…”

Section: H Rmentioning

confidence: 96%

Symmetric Jacobians

Bondt

2014

Open Mathematics

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“…There has been recently many interesting developments about this conjecture and we shall focuss in this article on a few of them to motivate the interest of specialists of differential equations. In particular, the problem was recently reduced to the case of symmetric jacobians ( [7] and [26]):…”

Section: The Jacobian Conjecturementioning

confidence: 99%

From Abel equations to Jacobian conjecture

Françoise

2014

Publicacions Matemàtiques

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This is a survey relating several subjects bridging algebraic differential equations and their integrability, pertubative approach based on algebraic moments, the Jacobian conjecture and optimal transport of measures defined on the complement of an arrangement of hyperplanes. This text was written in relation with Jaume Llibre's 60th birthday and it touches several fields in which Jaume gave important contributions. It also contains some results wich have not yet been published before.

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“…In [3], Bondt and Essen proved that the conjecture for the case F = C may be reduced to showing that the conjecture is true when the Jacobian matrix of the map H = (H 1 , . .…”

Section: Introductionmentioning

confidence: 99%

The Jacobian Conjecture and Partial Differential Equations

Yang¹

2021

Preprint

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The Jacobian conjecture over a field of characteristic zero is considered directly in view of the partial differential equations it introduces. Using the solutions of such partial differential equations, some new families of polynomial maps satisfying the conjecture in all dimensions and of arbitrarily high degrees are obtained. For such maps, the inverse maps of similar structures are readily constructed explicitly.

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A reduction of the Jacobian Conjecture to the symmetric case

Cited by 42 publications

References 12 publications

Symmetric Jacobians

Symmetric Jacobians

From Abel equations to Jacobian conjecture

The Jacobian Conjecture and Partial Differential Equations

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