Resultats globals: 36 registres trobats en 0.02 segons.
Articles, 36 registres trobats
Articles 36 registres trobats  1 - 10següentfinal  anar al registre:
1.
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  
2.
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  
3.
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  
4.
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  
5.
12 p, 781.7 KB Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática (Chile)) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática (Chile))
We study the number of limit cycles bifurcating from the origin of a Hamiltonian system of degree 4. We prove, using the averaging theory of order 7, that there are quartic polynomial systems close these Hamiltonian systems having 3 limit cycles.
2020 - 10.4153/S0008439519000626
Canadian mathematical bulletin, Vol. 63, Issue 3 (September 2020) , p. 547-561  
6.
11 p, 404.9 KB Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))
We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian H=(p21+p22)/2+1/P(q1,q2), being P(q1,q2) a homogeneous polynomial of degree 4 of one of the following forms ±q41, 4q31q2, ±6q21q22, ±(q21+q22)2, ±q22(6q21−q22), ±q22(6q21+q22), q41+6μq21q22−q42, −q41+6μq21q22+q42 with μ>−1/3 and μ≠1/3, and q41+6μq21q22+q42 with μ≠±1/3. [...]
2021 - 10.3934/dcdsb.2021228
Discrete and continuous dynamical systems. Series B, 2021  
7.
12 p, 751.4 KB Periodic solutions and their stability for some perturbed Hamiltonian systems / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa. Academia General Del Aire) ; Wade, Bruce A. (University of Louisiana at Lafayette. Mathematics Department (USA))
We deal with non-autonomous Hamiltonian systems of one degree of freedom. For such differential systems, we compute analytically some of their periodic solutions, together with their type of stability. [...]
2021 - 10.1142/S0219887821500134
International Journal of Geometric Methods in Modern Physics, Vol. 18, Issue 1 (January 2021) , art. 2150013  
8.
30 p, 951.8 KB On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can exhibit. Moreover, we analyze the possible configurations of these centers with respect to the invariant coordinate axes, and obtain that the real algebraic curve xy(a+bx+cy+dx2+exy+fy2)=h has at most four families of level ovals in R2 for all real parameters a,b,c,d,e,f and h.
2020 - 10.2140/pjm.2020.306.611
Pacific Journal of Mathematics, Vol. 306, Issue 2 (2020) , p. 611-644  
9.
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 documents
10.
31 p, 382.8 KB Integrability by separation of variables / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
We study the integrability in the Jacobi sense (integrability by separation of variables), of the Hamiltonian differential systems using the Levi-Civita Theorem. In particular we solve the Stark problem for N>3.
2020 - 10.1016/j.physd.2020.132523
Physica D. Nonlinear phenomena, Vol. 409 (August 2020) , art. 132523  

Articles : 36 registres trobats   1 - 10següentfinal  anar al registre:
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