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Depósito Digital de Documentos de la UAB Encontrados 6 registros  La búsqueda tardó 0.01 segundos. 
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.
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 documentos
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3.
13 p, 669.2 KB Isochronicity for trivial quintic and septic planar polynomial Hamiltonian systems / Braun, Francisco (Universidade Federal de Sâo Carlos Rod(Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (UFSCar(Brazil). Department of Physics, Chemistry and Mathematics)
In this paper we completely characterize trivial isochronous centers of degrees 5 and 7. Precisely, we provide formulas, up to linear change of coordinates, for the Hamiltonian H of the isochronous centers such that H =(f_1^2 f_2^2)/2 has degrees 6 and 8, and f = (f_1, f_2): R^2 R^2 is a polynomial map with D f = 1 and f(0,0) = (0,0).
2016 - 10.3934/dcds.2016029
Discrete and continuous dynamical systems. Series A, Vol. 36 Núm. 10 (2016) , p. 5245-5255  
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4.
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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5.
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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6.
17 p, 1.8 MB Half-Reeb components, Palais-Smale condition and global injectivity of local diffeomorphisms in R3 / Braun, Francisco (Universidade Federal de Sao Carlos. Departamento de Matemática) ; Venato-Santos, Jean (Universidade Federal de Uberlândia. Faculdade de Matemática)
Let F = (F1, F2, F3): R3 → R3 be a C∞ local diffeomorphism. We prove that each of the following conditions are sufficient to the global injectivity of F: A) The foliations FFi made up by the connected components of the level surfaces Fi = constant, consist of leaves without half-Reeb components induced by Fj , j ∈ {1, 2, 3} \ {i}, for i ∈ {1, 2, 3}. [...]
2014 - 10.5565/PUBLMAT_Extra14_04
Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 63-79  
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