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Resultats globals: 7 registres trobats en 0.02 segons.
Articles, 7 registres trobats
Articles 7 registres trobats  
1.
On the connection between global centers and global injectivity in the plane / Braun, Francisco (Universidade Federal de São Carlos. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this note we revisit a result of Sabatini relating global injectivity of polynomial maps to global centers in the plane. We deliver a generalization of this result for C maps defined on connected sets. [...]
2023 - 10.1007/s12591-023-00630-5
Differential Equations and Dynamical Systems, (July 2023)  
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2.
15 p, 628.2 KB A sufficient condition for the real Jacobian conjecture in R2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
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.
2021 - 10.1016/j.nonrwa.2021.103298
Nonlinear Analysis: Real World Applications, Vol. 60 (August 2021) , p. 103298  
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3.
9 p, 596.2 KB A new sufficient condition in order that the real Jacobian conjecture in R2 holds / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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 det⁡(DF(x,y)) = constant ≠ 0 and F(0,0) = (0,0) equivalent to the Jacobian conjecture.
2021 - 10.1016/j.jde.2021.01.038
Journal of differential equations, Vol. 281 (April 2021) , p. 333-340  
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4.
7 p, 285.2 KB New classes of polynomial maps satisfying the real Jacobian conjecture in R2 / Itikawa, Jackson (Universidade Federal de Rondônia. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ2. The first class is formed by the polynomials maps of the form (q(x) - p(y),q(y) + p(x)): ℝ2 → ℝ2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. [...]
2019 - 10.1590/0001-3765201920170627
Anais da Academia Brasileira de Ciencias, Vol. 91, Issue 2 (2019) , art. e20170627
2 documents
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5.
19 p, 414.8 KB The phase portrait of the Hamiltonian system associated to a Pinchuk map / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Braun, Francisco (Universidade Federal de São Carlos. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions, six of them of type strip and one annular.
2018 - 10.1590/0001-3765201820170829
Anais da Academia Brasileira de Ciencias, Vol. 90, Issue 3 (July-September 2018) , p. 2599-2616
2 documents
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6.
11 p, 694.7 KB A sufficient condition in order that the Real Jacobian Conjecture in R^2 holds / Braun, Francisco (Universidade Federal de Sâo Carlos Rod(Brasil). Departamento de Matemática) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let F=(f,g):\R^2\R^2 be a polynomial map such that DF(x) is different from zero for all x\R^2 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 the polynomials ff_x g g_x and f f_y g g_y do not have real linear factors in common.
2016 - 10.1016/j.jde.2015.12.011
Journal of differential equations, Vol. 260 (2016) , p. 5250-5258  
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7.
8 p, 263.7 KB A new qualitative proof of a result on the real Jacobian conjecture / Braun, Francisco (Universidade Federal de Sao Carlos Rod. Departamento de Matematica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let F = (f, g) : R → R be a polynomial map such that det DF (x) is different from zero for all x ∈ R^2 . We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of f and g, respectively. [...]
Let F = (f, g) : R2 → R2 be a polynomial map such that det DF (x) is different from zero for all x ∈ R2 . We assume that the degrees of f and g are equal. We denote by f and g the homogeneous part of higher degree of f and g, respectively. [...]
2015 - 10.1590/0001-3765201520130408
Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 3 (2015) , p. 1519-1524  
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