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UAB Digital Repository of Documents 12 records found  1 - 10next  jump to record: Search took 0.32 seconds. 
1.
7 p, 613.2 KB On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (Université de Bordj Bou Arréridj. Departement de Mathématiques (Algeria))
In this paper we study the existence and non-existence of limit cycles for the class of polynomial differential systems of the form ẋ=λx+Pn(x,y),ẏ=μy+Qn(x,y),where Pn and Qn are homogeneous polynomials of degree n.
2019 - 10.1016/j.aml.2019.07.002
Applied Mathematics Letters, Vol. 98 (December 2019) , p. 427-431  
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2.
7 p, 360.3 KB A note on a family of non-gravitational central force potentials in dimension one / Álvarez-Ramírez, Martha (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Matemáticas) ; Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya. Departament de Tecnologies Digitals i de la Informació) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; García, Alberto (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Matemáticas)
In this work, we study a one-parameter family of differential equations and the different scenarios that arise with the change of parameter. We remark that these are not bifurcations in the usual sense but a wider phenomenon related with changes of continuity or differentiability. [...]
2017 - 10.1016/j.aml.2017.04.020
Applied Mathematics Letters, Vol. 74 (December 2017) , p. 74-78  
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3.
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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4.
7 p, 289.4 KB Limit cycles of a second-order differential equation / Chen, Ting (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide an upper for the maximum number of limit cycles bifurcating from the periodic solutions of x=0, when we perturb this system as follows \ (1 ^m )Q(x,y) x=0, \] where >0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and =(y/x). [...]
2019 - 10.1016/j.aml.2018.08.015
Applied mathematics letters, Vol. 88 (2019) , p. 111-117  
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5.
5 p, 726.8 KB Limit cycles for a variant of a generalized Riccati equation / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (x, y = x) given by a variant of the generalized Riccati equation \[ x x^2n 1 x b x^4n 3=0, \] where b>0, b \R, n is a non--negative integer and is a small parameter. [...]
2017 - 10.1016/j.aml.2016.11.016
Applied mathematics letters, Vol. 68 (2017) , p. 76-79  
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6.
7 p, 731.3 KB On the Integrability of Liénard systems with a strong saddle / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the local analytic integrability for real Li\'enard systems, x=y-F(x), y= x, with F(0)=0 but F'(0)0, which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the [p:-q] resonant saddles. [...]
2017 - 10.1016/j.aml.2017.03.004
Applied mathematics letters, Vol. 70 (2017) , p. 39-45  
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7.
6 p, 643.0 KB On the analytic integrability of the cored galactic Hamiltonian / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide a complete characterization of the analytic first integrals of the cored galactic Hamiltonian.
2014 - 10.1016/j.aml.2014.03.001
Applied mathematics letters, Vol. 33 (2014) , p. 35-39  
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8.
8 p, 693.0 KB On the periodic orbits of the Third-order differential equation x ' ' '- x ' ' x'- x= F(x,x',x ' ') / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Roberto, Lucy Any (Ibilce - UNESP(Brasil). Departamento de Matemática)
In this paper we study the periodic orbits of the third-order differential equation x''' − µx'' + x' − µx = εF(x, x', x''), where ε is a small parameter and the function F is of class C2.
2013 - 10.1016/j.aml.2012.10.017
Applied mathematics letters, Vol. 26 (2013) , p. 425-430  
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9.
7 p, 591.8 KB A note on Liouvillian first integrals and invariant algebraic curves / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the existence and non-existence of finite invariant algebraic curves for complex planar polynomial differential system having a Liouvillian first integral.
2013 - 10.1016/j.aml.2012.09.008
Applied mathematics letters, Vol. 26 (2013) , p. 285-289  
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10.
8 p, 663.0 KB Generalized Weierstrass integrability for the complex differential equations dy/dx=a(x)y^4 b(x)y^3 c(x)y^2 d(x)y e(x) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the differential equations of the form dy/dx = a(x)y4 + b(x)y3 + c(x)y2 + d(x)y + e(x), where a, b, c, d, e are meromorphic functions in the variable x, that admits either a generalized Weierstrass first integral or a generalized Weierstrass inverse integrating factor.
2013 - 10.1016/j.aml.2013.03.018
Applied mathematics letters, Vol. 26 Núm. 8 (2013) , p. 836-841  
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