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Articles 42 registres trobats  anterior11 - 20següentfinal  anar al registre: La cerca s'ha fet en 0.01 segons. 
11.
16 p, 319.9 KB Limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points / Fernandes da Fonseca, Alexander (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil))
We study the existence of limit cycles in planar piecewise linear Hamiltonian systems with three zones without equilibrium points. In this scenario, we have shown that such systems have at most one crossing limit cycle.
2020 - 10.1142/S0218127420501576
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 11 (September 2020) , art. 2050157  
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12.
11 p, 320.0 KB A new algorithm for finding rational first integrals of polynomial vector fields / Ferragut Amengual, Antoni Manel (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Centre National de la Recherche Scientifique (França))
We present a new method to compute rational first integrals of planar polynomial vector fields. The algorithm is in general much faster than the usual methods and also allows to compute the remarkable curves associated to the rational first integral of the system.
2010 - 10.1007/s12346-010-0021-x
Qualitative theory of dynamical systems, Vol. 9, Issue 1-2 (November 2010) , p. 89-99  
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13.
13 p, 273.4 KB Quadratic perturbations of a quadratic reversible Lotka-Volterra system / Li, Chengzhi (Peking University. School of Mathematical Sciences (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0,0), (1,0), (2,0), (1,1) and (1,2).
2010 - 10.1007/s12346-010-0026-5
Qualitative theory of dynamical systems, Vol. 9, Issue 1-2 (November 2010) , p. 235-249  
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14.
14 p, 596.0 KB Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points / Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. [...]
2020 - 10.3390/MATH8050755
Mathematics, Vol. 8, Issue 5 (May 2020) , art. 755
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15.
14 p, 412.2 KB Topological classification of polynomial complex differential equations with all the critical points of centre type / Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
In this paper we study the global phase portrait of complex polynomial differential equations of degree n of the form z˙ = f(z), having all their critical points of center type. We give the exact number of topologically different phase portraits on the Poincaré disk when n ≤ 6 and, in the remaining cases, an upper bound for this number which only depends on n.
2010 - 10.1080/10236190903232654
Journal of Difference Equations and Applications, Vol. 16, Issue 5-6 (May 2010) , p. 411-423  
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16.
22 p, 1.3 MB A Bendixson-Dulac theorem for some piecewise systems / Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The Bendixson-Dulac Theorem provides a criterion to find upper bounds for the number of limit cycles in analytic differential systems. We extend this classical result to some classes of piecewise differential systems. [...]
2020 - 10.1088/1361-6544/ab6812
Nonlinearity, Vol. 33, Num. 5 (May 2020) , p. 2455-2480  
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17.
21 p, 459.5 KB On the computation of Darboux first integrals of a class of planar polynomial vector fields / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Galindo, Carlos (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Monserrat, Francisco (Universitat Politècnica de València. Institut Universitari de Matemàtica Pura i Aplicada)
We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏ri = 1fαii, where the αi's are positive real numbers and the fi's are polynomials defining curves with only one place at infinity. [...]
2019 - 10.1016/j.jmaa.2019.05.052
Journal of mathematical analysis and applications, Vol. 478, Issue 2 (October 2019) , p. 743-763  
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18.
7 p, 237.2 KB 24 crossing limit cycles in only one nest for piecewise cubic systems / Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work, we are interested in crossing limit cycles surrounding only one equilibrium point or a sliding segment. The studied systems are piecewise cubic polynomial defined in two zones separated by a straight line. [...]
2020 - 10.1016/j.aml.2019.106189
Applied Mathematics Letters, Vol. 103 (May 2020) , art. 106189  
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19.
35 p, 913.1 KB Phase portraits of linear type centers of polynomial hamiltonian systems with hamiltonian function of degree 5 of the form H = H1(x) + H2(y) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We study the phase portraits on the Poincaré disc for all the linear type centers of polynomial Hamiltonian systems of degree 5 with Hamiltonian function H(x, y) = H + H, where H = 1/2 x + a/3 x + a/4 x + a/5 x and H = 1/2 y + b/3 y + b/4 y + b/5 y as function of the six real parameters a, a, a, b, b and b with ab ≠ 0. [...]
2019 - 10.3934/dcds.2019004
Discrete and continuous dynamical systems. Series A, Vol. 39, Issue 1 (January 2019) , p. 75-113  
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20.
26 p, 687.0 KB Simultaneous bifurcation of limit cycles from a cubic piecewise center with two period annuli / Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of periodic orbits that bifurcate from a cubic polynomial vector field having two period annuli via piecewise perturbations. The cubic planar system (x',y')= (-y((x-1)² + y²),x((x-1)² + y²) has simultaneously a center at the origin and at infinity. [...]
2018 - 10.1016/j.jmaa.2017.12.072
Journal of mathematical analysis and applications, Vol. 461, issue 1 (May 2018) , p. 248-272  
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