TY - JOUR
TI - On the rational real Jacobian conjecture
AU - Campbell, Andrew
TI - On the rational real Jacobian conjecture
AB -  Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of Rn to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The birational case is proved and the Galois case clarified. Two known special cases of the Strong Real Jacobian Conjecture (SRJC) are generalized to the rational map context. For an invertible map, the associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. That disqualifies the Pinchuk counterexamples to the SRJC as candidates for invertibility.
VL - 2013
IS - Tom 51
PY - 2014
SN - 0083-4386
C1 - 2084-3828
SP - 7
EP - 15
UR - https://ejournals.eu/czasopismo/universitatis-iagellonicae-acta-mathematica/artykul/on-the-rational-real-jacobian-conjecture
KW - Real rational map
KW - Jacobian conjecture