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Depósito Digital de Documentos de la UAB Encontrados 9 registros  La búsqueda tardó 0.01 segundos. 
1.
16 p, 279.8 KB Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
A polynomial differential system of degree 2 has no global centers (that is, centers defined in all the plane except the fixed point). In this paper we characterize the global centers of cubic Hamiltonian systems symmetric with respect to the x-axis, and such that the center has purely imaginary eigenvalues.
2020
Electronic journal of differential equations, Vol. 2020 Núm. 57 (2020) , p. 1-14
2 documentos
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2.
15 p, 671.3 KB Integrability and zero-Hopf bifurcation in the Sprott A system / Barreira, Luis (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y, y˙=−x−yz, z˙=y²−a and the second one is to show that for a > 0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a = 0. [...]
2020 - 10.1016/j.bulsci.2020.102874
Bulletin des Sciences Mathematiques, Vol. 162 (September 2020) , art. 102874  
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3.
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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4.
13 p, 712.8 KB Limit cycles bifurcating from a zero-Hopf singularity in arbitrary dimension / Barreira, Luis (Instituto Superior Técnico (Portugal). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
We study the limit cycles which can bifurcate from a zero--Hopf singularity of a C^m 1 differential system in \R^n, i. e. from a singularity with eigenvalues b i and n-2 zeros for n 3. If this singularity is at the origin of coordinates and the Taylor expansion of the differential system at the origin without taking into account the linear terms starts with terms of order m, from the origin it can bifurcate s limit cycles with s \ 0,1, 2^n-3\ if m=2 (see LZ), with s \ 0,1, 3^n-2\ if m=3, with s 6^n-2 if m=4, and with s 4 5^n-2 if m=5. [...]
2018 - 10.1007/s11071-018-4115-3
Nonlinear dynamics, Vol. 92, issue 3 (May 2018) , p. 1159-1166  
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5.
17 p, 323.7 KB Periodic orbits near equilibria via averaging theory of second order / Barreira, Luis (Instituto Superior Técnico(Portugal). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico(Portugal). Departamento de Matemática)
Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. [...]
2012 - 10.3846/13926292.2012.736090
Mathematical Modelling and Analysis, Vol. 17 Núm. 5 (2012) , p. 715-731  
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6.
18 p, 730.8 KB Bifurcation of Limit cycles from a 4-dimensional center in R^m in resonance 1:N / Barreira, Luis (Universidade Técnica de Lisboa. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
For every positive integer N ≥ 2 we consider the linear differential center ˙x = Ax in Rm with eigenvalues ±i, ±N i and 0 with multiplicity m − 4. We perturb this linear center inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i. [...]
2012 - 10.1016/j.jmaa.2011.12.018
Journal of mathematical analysis and applications, Vol. 389 (2012) , p. 754-768  
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7.
15 p, 714.8 KB Limit cycles from a four-dimensional centre in R^m in resonance p:q / Barreira, Luis (Instituto Superior Técnico de Portugal. Departamento de Matematica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Instituto Superior Técnico de Portugal. Departamento de Matematica)
2012 - 10.1080/14689367.2012.722911
Dynamical Systems, Vol. 27 Núm. 4 (2012) , p. 459-474  
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8.
16 p, 637.2 KB Integrability and limit cycles of Moon-Rand system / Barreira, Luis (Universidade de Lisboa. Departamento de Matemática) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the Darboux integrability of the Moon-Rand polynomial differential system. Moreover we study the limit cycles of the perturbed Moon-Rand system bifurcating from the equilibrium point located at the origin, when it is perturbed inside the class of all quadratic polynomial differential systems in R3, and we prove that at first order in the perturbation parameter ε the perturbed system can exhibit one limit cycle, and that at second order it can exhibit four limit cycles bifurcating from the origin. [...]
2015 - 10.1016/j.ijnonlinmec.2014.11.029
International Journal of Non-Linear Mechanics, Vol. 69 (2015) , p. 129-136  
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9.
14 p, 317.2 KB Irregular sets for ratios of Birkhoff averages are residual / Barreira, Luis (Instituto Superior Técnico (Lisboa, Portugal). Departamento de Matemática) ; Li, Jinjun (Minnan Normal University. School of Mathematics and Statistics) ; Valls, Clàudia, 1973- (Instituto Superior Técnico (Lisboa, Portugal). Departamento de Matemática)
It follows from Birkhoff's Ergodic Theorem that the irregular set of points for which the Birkhff averages of a given continuous function diverge has zero measure with respect to any finite invariant measure. [...]
2014 - 10.5565/PUBLMAT_Extra14_03
Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 49-62  
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