3 citations · 6 across the 7 of their papers we have counts for
8 papers
Reduction Theorems for the Strong Real Jacobian Conjecture
L. Andrew Campbell
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 g…
On the Rational Real Jacobian Conjecture
L. Andrew Campbell
Jacobian conjectures (that nonsingular implies a global inverse) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant J…
Pinchuk Maps and Function Fields
L. Andrew Campbell
All counterexamples of Pinchuk type to the strong real Jacobian conjecture are shown to have rational function field extensions of degree six with no nontrivial automorphisms.
Pinchuk maps, function fields, and real Jacobian conjectures
L. Andrew Campbell
Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobia…
The Asymptotic Variety of a Pinchuk Map as a Polynomial Curve
L. Andrew Campbell
The asymptotic variety of a counterexample of Pinchuk type to the strong real Jacobian conjecture is explicitly described by low degree polynomials.
Iterated Images and the Plane Jacobian Conjecture
Ronen Peretz, Nguyen Van Chau, Carlos Gutierrez +1
We show that the iterated images of a Jacobian pair stabilize; that is, the k-th iterates of a polynomial map of complex two-space to itself with a nonzero constant Jacobian determ…