The sharp degree bound guaranteeing injectivity of real polynomial maps with non-zero Jacobian in two variables is 6.
Gwo ´zdziewicz, The real Jacobian conjecture for polynomials of degree 3, Ann
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A sharp degree bound in the real Jacobian conjecture
The sharp degree bound guaranteeing injectivity of real polynomial maps with non-zero Jacobian in two variables is 6.