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UAB Digital Repository of Documents 13 records found  1 - 10next  jump to record: Search took 0.00 seconds. 
1.
17 p, 334.7 KB The local cyclicity problem : Melnikov method using Lyapunov constants / Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor developments of the Lyapunov constants and the developments of the first Melnikov function near a non-degenerate monodromic equilibrium point, in the study of limit cycles of small-amplitude bifurcating from a quadratic centre. [...]
2022 - 10.1017/S0013091522000128
Proceedings of the Edinburgh Mathematical Society, Vol. 65 Issue 2 (May 2022) , p. 356-375  
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2.
22 p, 367.9 KB Lower bounds for the number of limit cycles in a generalised Rayleigh-Liénard oscillator / Euzébio, R (Federal University of Goiás. Institute of Mathematics and Statistics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tonon, Durval José (Federal University of Goiás. Institute of Mathematics and Statistics)
In this paper a generalised Rayleigh-Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. [...]
2022 - 10.1088/1361-6544/ac7691
Nonlinearity, Vol. 35, Issue 8 (August 2022) , p. 3883-3906  
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3.
16 p, 560.7 KB Hopf bifurcation in 3-dimensional polynomial vector fields / Sanchez Sanchez, Ivan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the local cyclicity of some polynomial vector fields in R3. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. [...]
2022 - 10.1016/j.cnsns.2021.106068
Communications in nonlinear science and numerical simulation, Vol. 105 (February 2022) , art. 106068  
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4.
21 p, 476.1 KB Lower bounds for the local cyclicity for families of centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we are interested on how the local cyclicity of a family of centers depends on the parameters. This fact, was pointed out in [21], to prove that there exists a family of cubic centers, labeled by CD12 31 in [25], with more local cyclicity than expected. [...]
2021 - 10.1016/j.jde.2020.11.035
Journal of differential equations, Vol. 275 (February 2021) , p. 309-331  
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5.
30 p, 468.7 KB Lower bounds for the local cyclicity of centers using high order developments and parallelization / Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. [...]
2021 - 10.1016/j.jde.2020.08.027
Journal of differential equations, Vol. 271 (January 2021) , p. 447-479  
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6.
9 p, 634.4 KB A note on the Lyapunov and period constants / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin of a weak focus or a non degenerated center for a family of planar polynomial vector fields is governed by the structure of the so called Lyapunov constants, that are polynomials in the parameters of the system. [...]
2020 - 10.1007/s12346-020-00375-4
Qualitative theory of dynamical systems, Vol. 19, Issue 1 (April 2020) , art. 44  
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7.
21 p, 834.1 KB Centers for generalized quintic polynominal differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
2017 - 10.1216/RMJ-2017-47-4-1097
The Rocky Mountain Journal of Mathematics, Vol. 47 Núm. 4 (2017) , p. 1097-1120  
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8.
20 p, 414.4 KB Center problem for systems with two monomial nonlinearities / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. [...]
2016 - 10.3934/cpaa.2016.15.577
Communications on pure & applied analysis, Vol. 15 Núm. 2 (2016) , p. 577-598  
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9.
6 p, 556.2 KB Analytic nilpotent centers as limits of nondegenerate centers revisited / García, Isaac (Universitat de Lleida. Departament de Matemàtica) ; Giacomini, Hector (Université de Tours(France). Laboratoire de Mathématiques et Physique Théorique) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues, and consequently the Poincaré-Liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers.
2016 - 10.1016/j.jmaa.2016.04.046
Journal of mathematical analysis and applications, Vol. 441 (2016) , p. 893-899  
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10.
14 p, 580.6 KB A method for characterizing nilpotent centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. [...]
2014 - 10.1016/j.jmaa.2013.12.013
Journal of mathematical analysis and applications, Vol. 413 (2014) , p. 537-545  
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