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Results overview: Found 23 records in 0.03 seconds.
Articles, 20 records found
Books and collections, 1 records found
Research literature, 2 records found
Articles 20 records found  1 - 10next  jump to record:
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.
28 p, 467.4 KB Invariant algebraic surfaces of polynomial vector fields in dimension three / Kruff, Niclas (Rheinisch-Westfälische Technische Hochschule Aachen. Lehrstuhl A für Mathematik) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Walcher, Sebastian (Rheinisch-Westfälische Technische Hochschule Aachen. Lehrstuhl A für Mathematik)
We discuss criteria for the nonexistence, existence and computation of invariant algebraic surfaces for three-dimensional complex polynomial vector fields, thus transferring a classical problem of Poincaré from dimension two to dimension three. [...]
2021 - 10.1007/s10884-021-10080-8
Journal of dynamics and differential equations, (October 2021)
2 documents
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4.
33 p, 842.3 KB Complete integrability of vector fields in RN / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We give necessary and sufficient conditions for the complete integrability of first order N-dimensional differential systems. We propose a new method to determine in the Jacobi Theorem the last N−1 first integral for the complete integrability of an N-dimensional differential system with N−2 independent first integrals and with a Jacobi multiplier. [...]
2021 - 10.1016/j.geomphys.2021.104308
Journal of geometry and physics, Vol. 168 (October 2021) , art. 104308  
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5.
24 p, 376.6 KB Three-dimensional Lotka-Volterra systems with 3:−1:2-Resonance / Aziz, Waleed (Tishk International University. Information Technology Department (Iraq)) ; Christopher, Colin (Plymouth University. School of Engineering, Computing and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka-Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. [...]
2021 - 10.1007/s00009-021-01809-2
Mediterranean Journal of Mathematics, Vol. 18, Issue 4 (August 2021) , art. 167  
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6.
15 p, 305.8 KB Integrability and linearizability of a family of three-dimensional quadratic systems / Aziz, Waleed (Salahaddin University-Erbil. Department of Mathematics (Iraq)) ; Amen, Azad (University of Raparin. College of Basic Education (Iraq)) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We consider a three-dimensional vector field with quadratic nonlinearities and in general none of the axis plane is invariant. For our investigation, we are interesting in the case of (Formula presented. [...]
2021 - 10.1080/14689367.2021.1893661
Dynamical Systems, Vol. 36, Issue 2 (2021) , p. 317-331  
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7.
30 p, 394.0 KB Monotone systems involving variable-order nonlocal operators / Yangari, Miguel (Escuela Politécnica Nacional,Ecuador. Departamento de Matemática)
In this paper, we study the existence and uniqueness of bounded viscosity solutions for parabolic Hamilton-Jacobi monotone systems in which the diffusion term is driven by variable-order nonlocal operators whose kernels depend on the space-time variable. [...]
2022 - 10.5565/PUBLMAT6612205
Publicacions matemàtiques, Vol. 66 Núm. 1 (2022) , p. 129-158 (Articles)  
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8.
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  
Detailed record -
9.
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  
Detailed record -
10.
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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Articles : 20 records found   1 - 10next  jump to record:
Books and collections 1 records found  
1.
4 p, 132.0 KB Analysis and numerical approximation of viscosity solutions with shocks : application to the plasma equation / Serna, Susana (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We consider a new class of Hamilton-Jacobi equations arising from the convective part of general Fokker-Planck equations ruled by a non-negative diffusion function that depends on the unknown and on the gradient of the unknown. [...]
2011 - 10.1063/1.3663455
Advances in Mathematical and Computational Methods: addressing modern challenges of science, technology, and society, 2011, p. 41-44  
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Research literature 2 records found  
1.
12 p, 316.4 KB Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time / Kornafel, Marta ; Centre de Recerca Matemàtica
The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. [...]
Centre de Recerca Matemàtica 2010 (Prepublicacions del Centre de Recerca Matemàtica ; 987)  
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2.
11 p, 197.6 KB Wiener type theorems for Jacobi series with nonnegative coefficients / Mhaskar, H. N. ; Tikhonov, Sergey Yu. ; Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer ajunt".
Centre de Recerca Matemàtica 2010 (Prepublicacions del Centre de Recerca Matemàtica ; 967)  
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