Browsing Articles publicats (Matemàtica) by Subject "Real Jacobian conjecture"

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A new sufficient condition in order that the real Jacobian conjecture in R2 holds

Giné, Jaume; Llibre, Jaume (Elsevier, 2021)

Let F = (f, g) : R2 → R2 be a polynomial map such that det(DF (x, y)) is nowhere zero and F (0, 0) = (0, 0). In this work we give a new sufficient condition for the injectivity of F . We also state a conjecture when ...
A sufficient condition in order that the real Jacobian conjecture in R^2 holds

Braun, Francisco; Giné, Jaume; Llibre, Jaume (Elsevier, 2016)

Let F=(f,g):R2→R2 be a polynomial map such that det⁡DF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of ...