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Articles, 167 registres trobats
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Articles 167 registres trobats  1 - 10següentfinal  anar al registre:
1.
Polynomial differential systems with even degree have no global centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
Let x˙=P(x,y), y˙=Q(x,y) be a differential system with P and Q real polynomials, and let d=max⁡{degP,degQ}. A singular point p of this differential system is a global center if R2∖{p} is filled with periodic orbits. [...]
2021 - 10.1016/j.jmaa.2021.125281
Journal of mathematical analysis and applications, Vol. 503, Issue 1 (November 2021) , art. 125281  
2.
Phase portraits of the complex Abel polynomial differential systems / 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 characterize the phase portraits of the complex Abel polynomial differential equations z˙=(z−a)(z−b)(z−c),with z∈C, a,b,c∈C. We give the complete description of their topological phase portraits in the Poincaré disc, i. [...]
2021 - 10.1016/j.chaos.2021.111050
Chaos, solitons and fractals, Vol. 148 (July 2021) , art. 111050  
3.
The Markus-Yamabe conjecture for discontinuous piecewise linear differential systems in Rn separated by a conic × Rn-2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In 1960 Markus and Yamabe made the conjecture that if a C1 differential system x˙=F(x) in Rn has a unique equilibrium point and DF(x) is Hurwitz for all x∈Rn, then the equilibrium point is a global attractor. [...]
2022 - 10.1007/s10884-021-10110-5
Journal of dynamics and differential equations, (January 2022)  
4.
The extended 16th Hilbert problem for discontinuous piecewise linear centers separated by a nonregular line / Esteban, Marina (Universidad de Sevilla. Departamento de Matemática Aplicada II) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The study of the piecewise linear differential systems goes back to Andronov, Vitt and Khaikin in 1920's, and nowadays such systems still continue to receive the attention of many researchers mainly due to their applications. [...]
2021 - 10.1142/S0218127421502254
International Journal of Bifurcation and Chaos, Vol. 31, Issue 15 (December 2021) , art. 2150225  
5.
Hamiltonian nilpotent saddles of linear plus cubic homogeneous polynomial vector fields / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin.
2022 - 10.1016/j.nonrwa.2021.103451
Nonlinear Analysis: Real World Applications, Vol. 64 (April 2022) , art. 103451  
6.
Weierstrass integrability of complex differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We characterize the complex differential equations of the form dydx=an(x)yn+an−1(x)yn−1+⋯+a1(x)y+a0(x), where a(x) are meromorphic functions in the variable x for j = 0,…,n that admit either a Weierstrass first integral or a Weierstrass inverse integrating factor.
2021 - 10.1007/s10114-021-8374-4
Acta Mathematica Sinica. English Series, Vol. 37, Issue 10 (October 2021) , p. 1497-1506  
7.
Periodic orbits for a generalized Hénon-Heiles Hamiltonian system with an additional singular gravitational term / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We study the periodic dynamics of the Hénon-Heiles Hamiltonian system with the additional singular gravitational term 1/(x2+y2). The Hénon-Heiles modelizes how stars move around a galactic center. [...]
2021 - 10.1209/0295-5075/134/60005
Europhysics Letters (EPL), Vol. 134, Issue 6 (June 2021) , art. 60005  
8.
On the existence of symmetric bicircular central configurations of the 3n-body problem / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Facultat de Ciències i Tecnologia) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In this paper, we consider central configurations of the planar 3n-body problem consisting of n masses at the vertices of a regular n-gon inscribed in a circle of radius r and 2n masses at the vertices of a second (not necessarily regular) concentric 2n-gon inscribed in a circle of radius ar which are symmetric in the sense that the set of positions of the 3n masses and the set of the corresponding masses are invariant under the action of a finite subgroup of O(2). [...]
2021 - 10.1007/s00332-021-09743-z
Journal of Nonlinear Science, Vol. 31, Issue 6 (December 2021) , art. 88  
9.
Global dynamics for the Szekeres system with non-zero cosmological constant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for the Einstein field equations in dimension four. It is a Hamiltonian system (with Hamiltonian H). [...]
2022 - 10.1016/j.dark.2022.100954
Physics of the Dark Universe, Vol. 35 (March 2022) , art. 100954  
10.
Discrete Melnikov functions / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented. ) having when (Formula presented. ) an open continuum of initial conditions such that the corresponding sequences are N-periodic. [...]
2021 - 10.1080/10236198.2021.1970147
Journal of Difference Equations and Applications, (August 2021)  

Articles : 167 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 2 registres trobats  
1.
129 p, 1.1 MB Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields / Evrim Colak, Ilker ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia, 1973-, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. [...]
In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2014  
2.
162 p, 983.1 KB Generalizaciones de la teoría de integrabilidad de Darboux para campos de vectores polinomiales / Bolaños Rivera, Yudy Marcela ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia, 1973-, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En matemáticas, la integrabilidad de los campos de vectores polinomiales ha sido objeto de estudio desde hace más de cien años. En 1878, Darboux dio unas condiciones que permiten establecer la existencia de una integral prime- ra para estos campos. [...]
In mathematics, the integrability of polynomial vector fields has been studied for more than one hundred years. In 1878, Darboux provided conditions to establish the existence of first integrals for these fields. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2013  

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