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Depósito Digital de Documentos de la UAB Encontrados 27 registros  1 - 10siguientefinal  ir al registro: La búsqueda tardó 0.01 segundos. 
1.
11 p, 404.9 KB Meromorphic integrability of the Hamiltonian systems with homogeneous potentials of degree -4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yuzhou (Sun Yat-sen University. School of Mathematics (China))
We characterize the meromorphic Liouville integrability of the Hamiltonian systems with Hamiltonian H=(p21+p22)/2+1/P(q1,q2), being P(q1,q2) a homogeneous polynomial of degree 4 of one of the following forms ±q41, 4q31q2, ±6q21q22, ±(q21+q22)2, ±q22(6q21−q22), ±q22(6q21+q22), q41+6μq21q22−q42, −q41+6μq21q22+q42 with μ>−1/3 and μ≠1/3, and q41+6μq21q22+q42 with μ≠±1/3. [...]
2021 - 10.3934/dcdsb.2021228
Discrete and continuous dynamical systems. Series B, 2021  
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2.
25 p, 954.3 KB Polynomial Hamiltonian systems of degree 3 with nilpotent saddles / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian planar polynomial vector fields of degree 3 symmetric with respect to the x−axis having a nilpotent saddle at the origin.
2021 - 10.3934/dcdsb.2020225
Discrete and continuous dynamical systems. Series B, Vol. 26, Issue 6 (June 2021) , p. 3209-3233  
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3.
12 p, 915.5 KB Phase portraits of the Higgins-Selkov system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
In this paper we study the dynamics of the Higgins-Selkov system x˙=1−xyγ,y˙=αy(xyγ−1−1), where α is a real parameter and γ > 1 is an integer. We classify the phase portraits of this system for γ = 3,4,5,6, in the Poincaré disc for all the values of the parameter α. [...]
2021 - 10.3934/dcdsb.2021039
Discrete and continuous dynamical systems. Series B, Vol. 26 (2021)  
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4.
14 p, 332.1 KB Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones / Itikawa, Jackson (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mereu, Ana Cristina (Universidade Federal de São Carlos. Departamento de Física, Química e Matemática (Brazil)) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação. Departamento de Matemática (Brazil))
We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. [...]
2017 - 10.3934/dcdsb.2017136
Discrete and continuous dynamical systems. Series B, Vol. 22, Issue 9 (November 2017) , p. 3259-3272  
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5.
26 p, 577.1 KB Periodic orbits of discrete and continuous dynamical systems via Poincaré-Miranda theorem / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
We present a systematic methodology to determine and locate analytically isolated periodic points of discrete and continuous dynamical systems with algebraic nature. We apply this method to a wide range of examples, including a one-parameter family of counterexamples to the discrete Markus-Yamabe conjecture (La Salle conjecture); the study of the low periods of a Lotka-Volterra-type map; the existence of three limit cycles for a piecewise linear planar vector field; a new counterexample of Kouchnirenko conjecture; and an alternative proof of the existence of a class of symmetric central configuration of the (1 + 4)-body problem.
2020 - 10.3934/dcdsb.2019259
Discrete and continuous dynamical systems. Series B, Vol. 25, Issue 2 (February 2020) , p. 651-670  
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6.
13 p, 326.6 KB Cyclicity of (1,3)-switching FF type equilibria / Chen, Xingwu (Sichuan University. Department of Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Weinian (Sichuan University. Department of Mathematics (China))
Hilbert's 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). [...]
2019 - 10.3934/dcdsb.2019153
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 12 (December 2019) , p. 6541-6552  
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7.
17 p, 414.8 KB Centers of discontinuous piecewise smooth quasi-homogeneous polynomial differential systems / Chen, Hebai (Fuzhou University. College of Mathematics and Computer Science (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
In this paper we investigate the center problem for the discontinuous piecewise smooth quasi-homogeneous but non-homogeneous polynomial differential systems. First, we provide sufficient and necessary conditions for the existence of a center in the discontinuous piecewise smooth quasi-homogeneous polynomial differential systems. [...]
2019 - 10.3934/dcdsb.2019150
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 12 (December 2019) , p. 6495-6509  
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8.
10 p, 632.5 KB Bifurcation of relative equilibria generated by a circular vortex path in a circular domain / Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Torres, Pedro J. (Universidad de Granada. Departamento de Matemática Aplicada)
We study the passive particle transport generated by a circular vortex path in a 2D ideal flow confined in a circular domain. Taking the strength and angular velocity of the vortex path as main parameters, the bifurcation scheme of relative equilibria is identified. [...]
2020 - 10.3934/dcdsb.2019265
Discrete and continuous dynamical systems. Series B, Vol. 25, Issue 2 (February 2020) , p. 749-760  
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9.
32 p, 2.2 MB On the limit cycles of a class of discontinuous piecewise linear differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; de Menezes, Lucyjane de A. S. (Universidade Federal de Goiás. Instituto de Matemática e Estatística (Brazil))
In this paper we consider discontinuous piecewise linear differential systems whose discontinuity set is a straight line L which does not pass through the origin. These systems are formed by two linear differential systems of the form ̇x= Ax ± b. [...]
2020 - 10.3934/dcdsb.2020005
Discrete and continuous dynamical systems. Series B, Vol. 25, Issue 5 (May 2020) , p. 1835-1858  
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10.
18 p, 773.2 KB On the limit cycles of planar discontinuous piecewise linear differential systems with a unique equilibrium / Li, Shimin (Guangdong University of Finance and Economics. School of Mathematics and Statistics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This paper deals with planar discontinuous piecewise linear differential systems with two zones separated by a vertical straight line x = k. We assume that the left linear differential system (x < k) and the right linear differential system (x > k) share the same equilibrium, which is located at the origin O(0, 0) without loss of generality. [...]
2019 - 10.3934/dcdsb.2019111
Discrete and continuous dynamical systems. Series B, Vol. 24, Issue 11 (November 2019) , p. 5885-5901  
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