Reduction theorems for the Strong Real Jacobian Conjecture

L. Andrew Campbell. "Reduction theorems for the Strong Real Jacobian Conjecture." Annales Polonici Mathematici 110.1 (2014): 1-11. <http://eudml.org/doc/280487>.

@article{L2014,
abstract = {Implementations of known reductions of the Strong Real Jacobian Conjecture (SRJC), to the case of an identity map plus cubic homogeneous or cubic linear terms, and to the case of gradient maps, are shown to preserve significant algebraic and geometric properties of the maps involved. That permits the separate formulation and reduction, though not so far the solution, of the SRJC for classes of nonsingular polynomial endomorphisms of real n-space that exclude the Pinchuk counterexamples to the SRJC, for instance those that induce rational function field extensions of a given fixed odd degree.},
author = {L. Andrew Campbell},
journal = {Annales Polonici Mathematici},
keywords = {real Jacobian conjecture; real analytic map; real polynomial map},
language = {eng},
number = {1},
pages = {1-11},
title = {Reduction theorems for the Strong Real Jacobian Conjecture},
url = {http://eudml.org/doc/280487},
volume = {110},
year = {2014},
}

TY - JOUR
AU - L. Andrew Campbell
TI - Reduction theorems for the Strong Real Jacobian Conjecture
JO - Annales Polonici Mathematici
PY - 2014
VL - 110
IS - 1
SP - 1
EP - 11
AB - Implementations of known reductions of the Strong Real Jacobian Conjecture (SRJC), to the case of an identity map plus cubic homogeneous or cubic linear terms, and to the case of gradient maps, are shown to preserve significant algebraic and geometric properties of the maps involved. That permits the separate formulation and reduction, though not so far the solution, of the SRJC for classes of nonsingular polynomial endomorphisms of real n-space that exclude the Pinchuk counterexamples to the SRJC, for instance those that induce rational function field extensions of a given fixed odd degree.
LA - eng
KW - real Jacobian conjecture; real analytic map; real polynomial map
UR - http://eudml.org/doc/280487
ER -