Results overview: Found 77 records in 0.02 seconds.
Articles, 74 records found
Research literature, 3 records found
Articles 74 records found  1 - 10nextend  jump to record:
1.
Critical periods in planar polynomial centers near a maximum number of cusps / De Maesschalck, Peter (Hasselt University) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. [...]
2024 - 10.1016/j.jde.2023.10.034
Journal of differential equations, Vol. 380 (January 2024) , p. 181-197  
2.
On the periodic orbits of the continuous-discontinuous piecewise differential systems with three pieces separated by two parallel straight lines / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)
During these last twenty years many papers have been published about the piecewise differential systems in the plane. The increasing interest on these kind of differential systems mainly is due to their big number of applications for modeling many natural phenomena. [...]
2023 - 10.1016/j.cnsns.2023.107421
Communications in nonlinear science and numerical simulation, Vol. 125 (October 2023) , art. 107421  
3.
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  
4.
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  
5.
15 p, 350.7 KB The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems / Barkat, Meriem (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems. [...]
2023 - 10.1007/s11071-022-07891-9
Nonlinear Dynamics, Vol. 111, Issue 2 (January 2023) , p. 1475-1484  
6.
A family of periodic orbits for the extended Hamiltonian system of the Van der Pol oscillator / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we show a new way of using the averaging theory for studying families of periodic orbits of a Hamiltonian system. We do this study computing a new family of periodic orbits of the extension of the Van der Pol oscillator to a Hamiltonian system of two degrees of freedom.
2023 - 10.1016/j.geomphys.2022.104705
Journal of geometry and physics, Vol. 183 (January 2023) , art. 104705  
7.
18 p, 887.5 KB Nilpotent bi-center in continuous piecewise Z2-equivariant cubic polynomial Hamiltonian systems / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Li, Shimin (Guangdong University of Finance and Economics. School of Statistics and Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
One of the classical and difficult problems in the theory of planar differential systems is to classify their centers. Here we classify the global phase portraits in the Poincaré disk of the class continuous piecewise differential systems separated by one straight line and formed by two cubic Hamiltonian systems with nilpotent bi-center at (± 1, 0). [...]
2022 - 10.1007/s11071-022-07631-z
Nonlinear Dynamics, Vol. 110, Issue 1 (September 2022) , p. 705-721  
8.
16 p, 458.9 KB Limit cycles of planar discontinuous piecewise linear Hamiltonian systems without equilibria separated by nonregular curves / Jimenez, Johana (Universidade Federal do Oeste da Bahia (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The problem of determining the existence, maximum number and positions of the limit cycles of the planar discontinuous piecewise linear differential systems is an important problem in the qualitative theory of differential systems. [...]
2022 - 10.1142/S021812742250184X
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 12 (September 2022) , art. 2250184  
9.
24 p, 1.3 MB Nilpotent center in a continuous piecewise quadratic polynomial Hamiltonian vector field / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian systems separated by the straight line x = 0, where these kinds of systems have a nilpotent center at (0, 0), which comes from the combination of two cusps of both Hamiltonian systems. [...]
2022 - 10.1142/S0218127422501164
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 8 (June 2022) , art. 2250116  
10.
18 p, 377.7 KB Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straight line, they have no limit cycles. [...]
2022 - 10.1080/14689367.2022.2037519
Dynamical Systems, Vol. 37, Issue 2 (February 2022) , p. 262-279  

Articles : 74 records found   1 - 10nextend  jump to record:
Research literature 3 records found  
1.
11 p, 391.7 KB Cerca de circuits Hamiltonians usant l'algorisme de Roberts i Flores / Roma Sau, Josep ; Borges, J. (Joaquim), (Joaquim), dir. (Universitat Autònoma de Barcelona. Departament d'Enginyeria de la Informació i de les Comunicacions) ; Universitat Autònoma de Barcelona. Escola d'Enginyeria
Des de fa més de 150 anys, quan W. R Hamilton va plantejar el concepte dels circuits hamiltonians, fins a dia d'avui, s'han descobert criteris per demostrar si un graf conté circuits hamiltonians, s'han desenvolupat algorismes per tal de trobar-los tots, però l'alta complexitat temporal que comporta resoldre aquestes qüestions en grafs no trivials fa que continuï essent un problema d'actualitat. [...]
For more than 150 years, When W. R Hamilton suggested the concept of Hamiltonian paths, until now, It has been discovered more judgements have proved that if a graph has Hamilitonian paths, as well as algorithms to get all the path's from the graph. [...]
Desde hace más de 150 años, cuando WR Hamilton planteó el concepto de los circuitos hamiltonianos, hasta día de hoy, se han descubierto criterios para demostrar si un grafo contiene circuitos hamiltonianos, se han desarrollado algoritmos para encontrarse todos, pero la alta complejidad temporal que conlleva resolver estas cuestiones en grafos no triviales hace que siga siendo un problema de actualidad. [...]

2017-02-07
Enginyeria Informàtica [958]  
2.
32 p, 619.7 KB Periodic orbits and nonintegrability of the Henon-Heiles Hamiltonian systems / Lembarki, Fatima Ezzahra ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
Dans la nature et dans la vie des hommes, de nombreux processus, sont en constante évolution. Nous parlons donc de systèmes dynamiques. Généralement ces changements incessants sont souvent difficiles à prédire et modéliser car ils surviennent de manière non linéaire et n'obéissent pas pleinement aux simples lois du hasard.
2011  
3.
129 p, 1.1 MB Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields / Colak, Ilker Evrim ; 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  

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