Classification of degree 2 polynomial automorphisms of C3.

Fornaess, John Erik, and Wu, He. "Classification of degree 2 polynomial automorphisms of C3.." Publicacions Matemàtiques 42.1 (1998): 195-210. <http://eudml.org/doc/41327>.

@article{Fornaess1998,
abstract = {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.},
author = {Fornaess, John Erik, Wu, He},
journal = {Publicacions Matemàtiques},
keywords = {Automorfismos; Polinomios de Jacobi; Determinantes; polynomial automorphism; Jacobian conjecture},
language = {eng},
number = {1},
pages = {195-210},
title = {Classification of degree 2 polynomial automorphisms of C3.},
url = {http://eudml.org/doc/41327},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Fornaess, John Erik
AU - Wu, He
TI - Classification of degree 2 polynomial automorphisms of C3.
JO - Publicacions Matemàtiques
PY - 1998
VL - 42
IS - 1
SP - 195
EP - 210
AB - 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.
LA - eng
KW - Automorfismos; Polinomios de Jacobi; Determinantes; polynomial automorphism; Jacobian conjecture
UR - http://eudml.org/doc/41327
ER -