Reduction theorems for the Strong Real Jacobian Conjecture

L. Andrew Campbell¹

¹908 Fire Dance Lane Palm Desert, CA 92211, U.S.A.

Annales Polonici Mathematici, Tome 110 (2014) no. 1, pp. 1-11

Résumé

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.

Détail

DOI : 10.4064/ap110-1-1

Keywords: implementations known reductions strong real jacobian conjecture srjc identity map plus cubic homogeneous cubic linear terms gradient maps shown preserve significant algebraic geometric properties maps involved permits separate formulation reduction though far solution srjc classes nonsingular polynomial endomorphisms real n space exclude pinchuk counterexamples srjc instance those induce rational function field extensions given fixed odd degree