Classification of degree 2 polynomial automorphisms of C3.
Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 195-210.
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 autormorphismE(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)⎧ H1(x, y, z) = (P(x, z) + ay, Q(z) + x, cz + d)⎪ H2(x, y, z) = (P(y, z) + ax, Q(y) + bz, y)⎨ H3(x, y, z) = (P(x, z) + ay, Q(x) + z, x)⎪ H4(x, y, z) = (P(x, y) + az, Q(y) + x, y)⎩ H5(x, y, z) = (P(x, y) + az, Q(x) + by, x)where P and Q are polynomials with max{deg(P), deg(Q)} = 2 and abc ≠ 0.
@article{PMATES_1998__42_1_41327,
author = {John Erik Fornaess and He Wu},
title = {Classification of degree 2 polynomial automorphisms of {C3.}},
journal = {Publicacions Matem\`atiques},
pages = {195-210},
volume = {42},
number = {1},
year = {1998},
zbl = {an:0923.58006},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41327/}
}
John Erik Fornaess; He Wu. Classification of degree 2 polynomial automorphisms of C3.. Publicacions Matemàtiques, Tome 42 (1998) no. 1, p. 195-210. https://geodesic-test.mathdoc.fr/item/PMATES_1998__42_1_41327/