New classes of polynomial maps satisfying the real jacobian conjecture in R2

Abstract

We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2. The first class is formed by the polynomials maps of the form (q(x) – p(y),q(y) + p(x)): ℝ2 → ℝ2 such that p and q are real polynomials satisfying p′ (x)q′ (x) ≠ 0. The second class is formed by polynomials maps (f,g): ℝ2 → ℝ2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.