Counterexamples to the Jacobian Conjecture from the viewpoint of lineability

Abstract

Algebraic genericity in the family of polynomial counterexamples to the recently solved Jacobian Conjecture for $N\ge 3$ is investigated. The notion of affine-coneability is introduced and it is shown that this family is affine-coneable and 1-lineable, but not 2-lineable. Semigroupability is further studied with respect to coordinatewise multiplication and composition.