Foliations and polynomial diffeomorphisms of R-3

Author(s)

Gutierrez, Carlos ^[1] ; Maquera, Carlos ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: MATHEMATISCHE ZEITSCHRIFT; v. 262, n. 3, p. 613-626, JUL 2009.
• Web of Science Citations: 2

Abstract

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of [f, g, h], made up by the level surfaces [k = constant], consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek's Jacobian Conjecture for polynomial maps of R(n). (AU)

• FAPESP's process: 03/03107-9 - Qualitative theory of differential equations and singularity theory
• Grantee: Carlos Teobaldo Gutierrez Vidalon
• Support Opportunities: Research Projects - Thematic Grants