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UAB Digital Repository of Documents 785 records found  previous11 - 20nextend  jump to record: Search took 0.02 seconds. 
11.
Nilpotent Bicenters in Continuous Piecewise Z2 -Equivariant Cubic Polynomial Hamiltonian Vector Fields : Cusp-Cusp Type / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics for a class of continuous piecewise Z2-equivariant cubic Hamiltonian vector fields with nilpotent bicenters at (±1, 0). We consider these polynomial vector fields with a challenging case where the bicenters (±1, 0) come from the combination of two nilpotent cusps separated by y = 0. [...]
2023 - 10.1142/S0218127423501389
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 12 (September 2023) , art. 2350138  
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12.
18 p, 334.8 KB Limit cycles of linear vector fields on (S2)m ×Rn / Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is well known that linear vector fields defined in Rn cannot have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form (S2)m × Rn when such vector fields are perturbed inside the class of all linear vector fields. [...]
2023 - 10.2140/pjm.2023.324.249
Pacific Journal of Mathematics, Vol. 324, Issue 2 (June 2023) , p. 249-263  
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13.
13 p, 959.5 KB Symmetric Phase Portraits of Homogeneous Polynomial Hamiltonian Systems of Degree 1, 2, 3, 4, and 5 with Finitely Many Equilibria / Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Roughly speaking, the Poincaré disc D2 is the closed disc centered at the origin of the coordinates of R2, where the whole of R2 is identified with the interior of D2 and the circle of the boundary of D2 is identified with the infinity of R2, because in the plane R2, we can go to infinity in as many directions as points have the circle. [...]
2023 - 10.3390/sym15081476
Symmetry, Vol. 15, Issue 8 (August 2023) , art. 1476  
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14.
58 p, 6.6 MB Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems / Li, Jie (Southwest Petroleum University. School of Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. [...]
2023 - 10.1007/s12591-023-00666-7
Differential Equations and Dynamical Systems, (November 2023)  
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15.
7 p, 3.9 MB Zero-Hopf bifurcation in the Chua's circuit / Ginoux, Jean-Marc (Université de Toulon. Laboratoire LSIS) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
An equilibrium point of a differential system in R 3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. [...]
2023 - 10.1063/5.0137020
Journal of Mathematical Physics, Vol. 64, Issue 7 (July 2023) , art. 72701  
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16.
19 p, 403.3 KB The Free Euler Rigid Body Revisited / Jiménez-Lara, Lidia (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Física) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We review from a different perspective the approach and solution to the torque-free Euler equations, also called the free asymmetric top equations. We aim to simplify and broaden the study of the asymmetric free rigid body. [...]
2023 - 10.3390/dynamics3030032
Dynamics, Vol. 3, Issue 3 (September 2023) , p. 603-621  
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17.
18 p, 772.0 KB Phase Portraits of Families VII and VIII of the Quadratic Systems / Cairó, Laurent (Université d'Orleans. Institut Denis Poisson) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications. [...]
2023 - 10.3390/axioms12080756
Axioms, Vol. 12, Issue 8 (August 2023) , art. 756  
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18.
On the indices of singular points for planar bounded piecewise smooth polynomial vector field / Li, Shimin (Hangzhou Normal University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Sun, Xianbo (Hangzhou Normal University. School of Mathematics)
We prove that for any piecewise-smooth bounded polynomial vector field in R2 with finitely many finite H-singular points (which include singular points, hyperbolic pseudo-equilibria and two fold singularities), the sum of the indices of all its finite H-singular points is 1.
2023 - 10.1016/j.nahs.2023.101350
Nonlinear Analysis: Hybrid Systems, Vol. 49 (August 2023) , art. 101350  
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19.
Nonexistence and Uniqueness of Limit Cycles in a Class of Three-Dimensional Piecewise Linear Differential Systems / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Huang, Lihong (Changsha University. College of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
During the last twenty years there has been increasing interest in studying the piecewise differential systems, mainly due to their many applications in natural science and technology. Up to now the most studied differential systems are in dimension two, here we study them in dimension three. [...]
2023 - 10.1142/S021812742350075X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 33, Issue 6 (May 2023) , art. 2350075  
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20.
Limit cycles of a continuous piecewise differential system formed by a quadratic center and two linear centers / Anacleto, Maria Elisa (Universidad del Bío-Bío. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
The study of limit cycles of planar differential systems is one of the main and difficult problems for understanding their dynamics. Thus the objective of this paper is to study the limit cycles of continuous piecewise differential systems in the plane separated by a non-regular line Σ. [...]
2023 - 10.1007/s40590-023-00501-7
Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 2 (July 2023) , art. 29  
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UAB Digital Repository of Documents : 785 records found   previous11 - 20nextend  jump to record:
See also: similar author names
1 Llibre, J.M.
797 Llibre, Jaume
797 Llibre, Jaume
2 Llibre, Jaume, 0000-0002-9511-5999
2 Llibre, Jaume, 0000-0002-9511-5999
5 Llibre, Josep M.
14 Llibre, Josep M..
1 Llibre, Josep Ma
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