Reduction theorems for the Strong Real Jacobian Conjecture
Tom 110 / 2014
Annales Polonici Mathematici 110 (2014), 1-11 MSC: Primary 14R15; Secondary 14E05, 14P10. DOI: 10.4064/ap110-1-1
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.