Classification of degree 2 polynomial automorphisms of C.
For the family of degree at most 2 polynomial self-maps of C3 with nowhere vanishing Jacobian determinant, we give the following classification: for any such map f, it is affinely conjugate to one of the following maps: (i) An affine automorphism; (ii) An elementary polynomial autormorphism E(x, y, z) = (P(y, z) + ax, Q(z) + by, cz + d), where P and Q are polynomials with max{deg(P), deg(Q)} = 2 and abc ≠ 0. (iii) ...