# Classification of degree 2 polynomial automorphisms of C3.

Publicacions Matemàtiques (1998)

- Volume: 42, Issue: 1, page 195-210
- ISSN: 0214-1493

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topFornaess, 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 -