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Dipòsit Digital de Documents de la UAB 79 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.01 segons. 
1.
28 p, 448.6 KB Differential Galois theory and non-integrability of planar polynomial vector fields / Acosta-Humánez, Primitivo B. (Universidad Simón Bolívar(Colombia). Facultad de Ciencias Básicas y Biomédicas) ; Tomás Lázao, J. (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Morales-Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica)
We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. [...]
2018 - 10.1016/j.jde.2018.02.016
Journal of differential equations, Vol. 264, issue 12 (June 2018) , p. 7183-7212  
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2.
10 p, 362.5 KB A proof of Bertrand’s theorem using the theory of isochronous potentials / Ortega, Rafael (Universidad de Granada. Departamento de Matemática Aplicada) ; Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada)
We give an alternative proof for the celebrated Bertrand’s theorem as a corollary of the isochronicity of a certain family of centers.
2018 - 10.1007/s10884-018-9676-9
Journal of dynamics and differential equations, Published online May 2018  
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3.
15 p, 468.0 KB A criticality result for polycycles in a family of quadratic reversible centers / Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada) ; Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d’Enginyeria Informàtica i Matemàtiques)
We consider the family of dehomogenized Loud's centers Xµ_=y(x-1)∂ₓ + (x + Dx² + Fy²)_y, where µ=(D,F)єR², and we study the number of critical periodic orbits that emerge or dissapear from the polycycle at the boundary of the period annulus. [...]
2018 - 10.1016/j.jde.2018.01.042
Journal of differential equations, Vol. 264, issue 11 (June 2018) , p. 6585-6602  
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4.
14 p, 238.1 KB Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lopes, Bruno D. (Universidade Estadual de Campinas (Brasil). Instituto de Matemática, Estatística e Computação Científica) ; De Moraes, Jaime R. (Universidad Estatal de Mato Grosso del Sur (Brasil))
In this paper we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. [...]
2018
Electronic journal of differential equations, Vol. 2018, No. 118 (2018) , p. 1-14  
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5.
23 p, 533.7 KB Analytic tools to bound the criticality at the outer boundary of the period annulus / Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rojas, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
In this paper we consider planar potential differential systems and we study the bifurcation of critical periodic orbits from the outer boundary of the period annulus of a center. In the literature the usual approach to tackle this problem is to obtain a uniform asymptotic expansion of the period function near the outer boundary. [...]
2018 - 10.1007/s10884-016-9559-x
Journal of dynamics and differential equations, Vol. 30, issue 3 (Sep. 2018) , p. 883-909  
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6.
25 p, 473.1 KB Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities / Huang, Jianfeng (Jinan University. Department of Mathematics) ; Liang, Haihua (Guangdong Polytechnic Normal University. School of Mathematics and Systems Science) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the limit cycles of the planar polynomial differential systems * x=ax-y P_n(x,y),\\ y=x ay Q_n(x,y), * where P_n and Q_n are homogeneous polynomials of degree n2, and a R. Consider the functions * &()=P_n() Q_n()\\ &()=Q_n()-P_n()\\ &_1()=a()-(),\\ &_2()=(n-1)(2a()-()) '(). [...]
2018 - 10.1016/j.jde.2018.05.019
Journal of differential equations, Vol. 265, issue 9 (Nov. 2018) , p. 3888-3913  
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7.
15 p, 625.2 KB Centers and uniform isochronous centers of planar polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat de Barcelona) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
For planar polynomial vector fields of the form \[ (-y X(x,y)) x (x Y(x,y)) y, \] where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers.
2018 - 10.1007/s10884-018-9672-0
Journal of dynamics and differential equations, Vol. 30, issue 3 (Sep. 2018) , p. 1295-1310  
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8.
7 p, 170.1 KB Normal forms and hyperbolic algebraic limit cycles for a class of polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàticaa)
We study the normal forms of polynomial systems having a set of invariant algebraic curves with singular points. We provide sufficient conditions for the existence of hyperbolic algebraic limit cycles.
2018
Electronic journal of differential equations, Vol. 2018, no. 83 (2018) , p. 1-7  
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9.
24 p, 759.4 KB Global phase portraits for quadratic systems with a hyperbola and a straight line as invariant algebraic curves / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Yu, Jiang (Shanghai Jiao Tong University. Department of Mathematics)
In this article we consider a class of quadratic polynomial differential systems in the plane having a hyperbola and a straight line as invariant algebraic curves, and we classify all its phase portraits. [...]
2018
Electronic journal of differential equations, Vol. 141 (2018) , p. 1-19  
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10.
24 p, 357.3 KB On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. [...]
2017 - 10.1016/j.jde.2017.08.003
Journal of Differential Equations, Vol. 263 (2017) , p. 7099-7122  
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