Results 1 to 10 of about 560 (193)

A new qualitative proof of a result on the real jacobian conjecture [PDF]

Anais da Academia Brasileira de Ciências, 2015
Let F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively.
FRANCISCO BRAUN, JAUME LLIBRE
doaj   +11 more sources

New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2 [PDF]

Anais da Academia Brasileira de Ciências, 2019
: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'
JACKSON ITIKAWA, JAUME LLIBRE
doaj   +6 more sources

A sufficient condition for the real Jacobian conjecture in R2

Nonlinear Analysis: Real World Applications, 2021
Let F = (f,g): R2 → R2 be a polynomial map such that detDF (x,y) is different from zero for all (x,y) ∈ R2. We provide some new sufficient conditions for the injectivity of F. The proofs are based on the qualitative theory of differential equations.
Claudia Valls, Jaume Llibre
exaly   +4 more sources

A new sufficient condition in order that the real Jacobian conjecture in R 2 holds

Journal of Differential Equations, 2021
The first author is partially supported by a MINECO/FEDER grant number MTM2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is partially supported by the Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER), the Agència de Gestió d'Ajuts ...
Jaume Gine, Jaume Llibre
exaly   +5 more sources

Diffeomorphic real-analytic maps and the Jacobian Conjecture

Mathematical and Computer Modelling, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +2 more sources

Remarks on the Real Jacobian Conjecture and Samuelson maps

Applied Mathematics Letters, 1997
A map \(F:\mathbb R^n\to\mathbb R^n\) of class \(C^1\) is called a Samuelson map if and only if the all leading principal minors \(\mu_i:=\det\frac{\partial(f_1,\dots,f_i)}{\partial(x_1,\dots,x_i)}, \;i=1,\dots,n\), of the Jacobi matrix of \(F\) vanish nowhere.
exaly   +3 more sources

A note on sufficient conditions for the real Jacobian conjecture in R^2

Electronic Journal of Differential Equations
The real Jacobian conjecture in $\mathbb{R}^2$ claims that if $F=(f,g):\mathbb{R}^2 \to \mathbb{R}^2$ is a polynomial map such that $ \det DF(x,y)\neq 0 $ for all $(x,y)\in \mathbb{R}^2$, then $F$ is globally injective.
Xiuli Cen, Kangnong Hu, Yuzhou Tian
doaj   +2 more sources

The real jacobian conjecture on $\R^2$ is true when one of the components has degree 3

Discrete and Continuous Dynamical Systems, 2010
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FRANCISCO Braun
exaly   +3 more sources

A new characterization of the Jacobian conjecture in the real plane and some consequences

Discrete and Continuous Dynamical Systems - Series S
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Isaac A Garcia, Jaume Gine
exaly   +3 more sources

New sufficient condition for the two-dimensional real Jacobian conjecture through the Newton diagram

Journal of Differential Equations
The present paper is devoted to investigating the two-dimensional real Jacobian conjecture. This conjecture claims that if $F=\left(f,g\right):\mathbb{R}^2\rightarrow \mathbb{R}^2$ is a polynomial map with $\det DF\left(x,y\right)\ne0$ for all $\left(x,y\right)\in\mathbb{R}^2$, then $F$ is globally injective.
Xiuli Cen
exaly   +4 more sources