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Resultats globals: 8 registres trobats en 0.01 segons.
Articles, 8 registres trobats
Articles 8 registres trobats  
1.
42 p, 672.9 KB The improved Euler-Jacobi formula and the planar cubic polynomial vector fields in ℝ2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The new Euler-Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. [...]
2022 - 10.1080/14689367.2022.2066508
Dynamical Systems, Vol. 37, Issue 3 (2022) , p. 403-443  
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2.
11 p, 285.4 KB Twin polynomial vector fields of arbitrary degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In this paper we study polynomial vector fields on C2 of degree larger than 2 with n2 isolated singularities. More precisely, we show that if two polynomial vector fields share n2−1 singularities with the same spectra (trace and determinant) and from these singularities n2−2 have the same positions, then both vector fields have identical position and spectra at all the singularities. [...]
2022 - 10.1007/s00574-021-00259-4
Bulletin of the Brazilian Mathematical Society, Vol. 53, Issue 1 (March 2022) , p. 295-306  
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3.
14 p, 598.2 KB Configurations of the topological indices of the planar polynomial differential systems of degree (2, m) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems x˙ = P(x, y), y˙ = Q(x, y) with degree of P equal to 2 and degree of Q equal to m when these systems have 2m finite singular points.
2021 - 10.1007/s00025-020-01322-0
Results in Mathematics, Vol. 76, Issue 1 (March 2021) , art. 21  
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4.
36 p, 651.2 KB On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.
2020 - 10.1007/s12346-020-00435-9
Qualitative theory of dynamical systems, Vol. 19, Issue 3 (December 2020) , art. 96  
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5.
8 p, 544.8 KB The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
The Euler-Jacobi formula provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar quadratic-quartic polynomial differential systems when these systems have eight finite singular points.
2021 - 10.1090/proc/15257
Proceedings of the American Mathematical Society, Vol. 149, Issue 1 (January 2021) , p. 135-141  
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6.
20 p, 782.2 KB On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems x˙=P(x,y,z), y˙=Q(x,y,z), z˙=R(x,y,z) with degrees of P, Q and R equal to two when these systems have the maximum number of isolated singular points, i. [...]
2020 - 10.1016/j.jde.2020.07.022
Journal of differential equations, Vol. 269, Issue 12 (December 2020) , p. 10571-10586  
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7.
9 p, 281.5 KB Bounded polynomial vector fields in R2 and Rn / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We characterize the bounded polynomial vector fields in R2. Additionally we provide a necessary condition but not sufficient which must be satisfied by bounded polynomial vector fields in Rn.
2020 - 10.1016/j.jde.2019.10.023
Journal of differential equations, Vol. 268, Issue 8 (April 2020) , p. 4416-4422  
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8.
13 p, 342.5 KB The index of singularities of vector fields and finite jets / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Saghin, Radu (Universitat Autònoma de Barcelona. Centre de Recerca per a l'Educació Científica i Matemàtica)
We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.
2011 - 10.1016/j.jde.2011.04.015
Journal of differential equations, Vol. 251 (2011) , p. 2822-2832  
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