2025-08-28
10:49 |
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2025-07-28
14:24 |
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Quadratic vector fields in class I
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Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Chen, Hebai (Central South University. School of Mathematics and Statistics (China)) ;
Ferrer, Lluc Manel (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Jia, Man (Central South University. School of Mathematics and Statistics (China))
In [Ye et al. , Theory of Limit Cycles, 1986], quadratic systems are classified into three different normal forms (I, II and III) with increasing number of parameters. The simplest family is I and even several subfamilies of it have been studied, and some global attempts have been done, up to this paper, the full study was still undone. [...]
2025 -  10.1080/14689367.2024.2436223
Dynamical Systems, Vol. 40, Issue 2 (2025) , p. 191-222
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2025-07-28
14:24 |
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2025-07-28
14:24 |
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On the Limit Cycles Bifurcating from the Periodic Orbits of a Hamiltonian System
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Anacona, Gerardo H. (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Freitas, Bruno (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
This paper concerns the weak 16th Hilbert problem and considers the Hamiltonian center a: = -y2n-1, a: = x2n-1, and we perturb it by all polynomials of degree 2n-1 for n = 2, 3, 4, 5, 6, 7, 8. We prove that the maximum number of limit cycles that can bifurcate from the periodic orbits of this center for n = 2, 3, 4, 5, 6, 7, 8, under the mentioned perturbations and using the averaging theory of first order, is 1, 4, 3, 2, 5, 6, 7, respectively.
2025 - 10.1142/S0218127425500403
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 35, Issue 4 (March 2025) , art. 2550040
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2025-07-28
14:24 |
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2025-07-28
14:24 |
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2025-07-28
14:24 |
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On Nested Central Configurations of the 3n Body Problem
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Barrabés Vera, Esther (Universitat de Girona) ;
Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya) ;
Fernandes, Antonio Carlos (Universidade Federal de Itajubá. Instituto de Matemática e Computação) ;
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
In this work, we consider the existence of (3, n)-crowns in the classical Newtonian 3n-body problem, which are central configurations formed by three groups of n bodies with the same mass within each group, located at the vertices of three concentric regular polygons. [...]
2025 - 10.1007/s00332-025-10162-7
Journal of Nonlinear Science, Vol. 35, Issue 4 (August 2025) , art. 67
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2025-07-09
15:14 |
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2025-07-09
12:45 |
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67 p, 999.8 KB |
Parabolic Saddles and Newhouse Domains in Celestial Mechanics
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Garrido, Miguel (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Martín, Pau (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ;
Paradela, Jaime (University of Maryland. Department of Mathematics)
In McGehee (J Differ Equ 14:70-88, 1973) McGehee introduced a compactification of the phase space of the restricted 3-body problem by gluing a manifold of periodic orbits "at infinity". Although from the dynamical point of view these periodic orbits are parabolic (the linearization of the Poincaré map is the identity matrix), one of them, denoted here by O, possesses stable and unstable manifolds which, moreover, separate the regions of bounded and unbounded motion. [...]
2025 - 10.1007/s00220-025-05299-1
Communications in mathematical physics, Vol. 406 (June 2025) , art. 173
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2025-07-03
10:03 |
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