Dipòsit Digital de Documents de la UAB 142 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.01 segons. 
1.
58 p, 6.6 MB Phase Portraits of a Class of Continuous Piecewise Linear Differential Systems / Li, Jie (Southwest Petroleum University. School of Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The phase portraits of the planar linear differential systems are very well known. This is not the case for the phase portraits of the planar continuous piecewise linear differential systems. In this paper we classify the phase portraits of the class of planar continuous piecewise linear differential systems of the form x˙=a|x|+by+c,y˙=α|x|+βy+γ, in the Poincaré disc when aβ- bα≠ 0, and prove the existence and uniqueness of limit cycles. [...]
2023 - 10.1007/s12591-023-00666-7
Differential Equations and Dynamical Systems, (November 2023)  
2.
88 p, 4.4 MB Structurally Unstable Quadratic Vector Fields of Codimension Two : Families Possessing One Finite Saddle-Node and a Separatrix Connection / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This paper is part of a series of works whose ultimate goal is the complete classification of phase portraits of quadratic differential systems in the plane modulo limit cycles. It is estimated that the total number may be around 2000, so the work to find them all must be split in different papers in a systematic way so to assure the completeness of the study and also the non intersection among them. [...]
2024 - 10.1007/s12346-023-00882-0
Qualitative theory of dynamical systems, Vol. 23, Issue 1 (February 2024) , art. 40  
3.
11 p, 281.1 KB Cyclicity Near Infinity in Piecewise Linear Vector Fields Having a Nonregular Switching Line / Bastos, Jefferson L. R. (Universidade Estadual Paulista. Departamento de Matemática) ; Buzzi, Claudio (Universidade Estadual Paulista. Departamento de Matemática) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we recover the best lower bound for the number of limit cycles in the planar piecewise linear class when one vector field is defined in the first quadrant and a second one in the others. [...]
2023 - 10.1007/s12346-023-00817-9
Qualitative theory of dynamical systems, Vol. 22, Issue 4 (December 2023) , art. 125  
4.
Number of limit cycles for planar systems with invariant algebraic curves / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Centre National de la Recherche Scientifique. Université de Tours. Institut Denis Poisson)
For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We present a general approach to prove non-existence of periodic orbits not contained in this given algebraic curve. [...]
2023 - 10.1007/s12346-023-00746-7
Qualitative theory of dynamical systems, Vol. 22, Issue 2 (June 2023) , art. 44  
5.
On the connection between global centers and global injectivity in the plane / Braun, Francisco (Universidade Federal de São Carlos. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this note we revisit a result of Sabatini relating global injectivity of polynomial maps to global centers in the plane. We deliver a generalization of this result for C maps defined on connected sets. [...]
2023 - 10.1007/s12591-023-00630-5
Differential Equations and Dynamical Systems, (July 2023)  
6.
42 p, 672.9 KB The improved Euler-Jacobi formula and the planar cubic polynomial vector fields in ℝ2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The new Euler-Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. [...]
2022 - 10.1080/14689367.2022.2066508
Dynamical Systems, Vol. 37, Issue 3 (2022) , p. 403-443  
7.
17 p, 375.4 KB Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres / Buzzi, Claudio (Universidade Estadual Paulista Julio de Mesquita Filho. Departamento de Matemática) ; Carvalho, Yagor Romano (Universidade de São Paulo. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
These last years an increasing interest appeared in studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. The understanding of the dynamics of these systems has many difficulties. [...]
2022 - 10.1080/14689367.2022.2122779
Dynamical Systems, Vol. 37, Issue 4 (2022) , p. 710-728  
8.
28 p, 592.1 KB Transcritical bifurcation at infinity in planar piecewise polynomial differential systems with two zones / de Carvalho Braga, Denis (Universidade Federal de Itajubá. Instituto de Matemática e Computação) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mello, Luis Fernando (Universidade Federal de Itajubá. Instituto de Matemática e Computação)
We present a general mechanism of generation of limit cycles in planar piecewise polynomial differential systems with two zones by means of a transcritical bifurcation at infinity and from a global centre. [...]
2022 - 10.1080/14689367.2022.2092454
Dynamical Systems, Vol. 37, Issue 4 (August 2022) , p. 578-602  
9.
16 p, 409.5 KB Phase portraits of the Selkov model in the Poincaré disc / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
In this paper we classify the phase portraits in the Poincaré disc of the Selkov model for the glycolysis process x˙ = −x + ay + x2y, y˙ = b − ay − x2y, in function of its parameters a, b ∈ R. [...]
2022 - 10.3934/dcdsb.2022056
Discrete and Continuous Dynamical Systems - B, Vol. 27, Issue 12 (December 2022) , p. 7607-7623  
10.
17 p, 387.7 KB Convexity and symmetry of central configurations in the five-body problem : Lagrange plus two / Barrabés Vera, Esther (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística) ; Cors Iglesias, Josep Maria (Universitat Politècnica de Catalunya. Departament de Matemàtiques) ; Fernandes, Antonio Carlos (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática (Chile))
We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations. [...]
2021 - 10.1007/s12346-021-00504-7
Qualitative theory of dynamical systems, Vol. 20, Issue 3 (November 2021) , art. 63  

Dipòsit Digital de Documents de la UAB : 142 registres trobats   1 - 10següentfinal  anar al registre:
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