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 x + H over ℂ such that satisfies all symmetries of the square, where H is homogeneous of arbitrary degree d ≥ 3.
@article{bwmeta1.element.doi-10_2478_s11533-013-0393-7,
author = {Michiel Bondt},
title = {Symmetric Jacobians},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {787-800},
zbl = {1307.14086},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0393-7}
}
Michiel Bondt. Symmetric Jacobians. Open Mathematics, Tome 12 (2014) pp. 787-800. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0393-7/
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