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UAB Digital Repository of Documents 785 records found  beginprevious21 - 30nextend  jump to record: Search took 0.00 seconds. 
21.
35 p, 627.1 KB Criteria on the existence of limit cycles in planar polynomial differential systems / 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)
We summarize known criteria for the non-existence, existence and on the number of limit cycles of autonomous real planar polynomial differential systems, and also provide new results. We give examples of systems which realize the maximum number of limit cycles provided by each criterion. [...]
2022 - 10.1016/j.exmath.2022.09.002
Expositiones Mathematicae, Vol. 40, Issue 4 (December 2022) , p. 1049-1083  
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22.
11 p, 296.4 KB On the Periodic Orbits of the Perturbed Two- and Three-Body Problems / Abouelmagd, Elbaz I. (National Research Institute of Astronomy and Geophysics. Astronomy Department (Egypt)) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work, a perturbed system of the restricted three-body problem is derived when the perturbation forces are conservative alongside the corresponding mean motion of two primaries bodies. Thus, we have proved that the first and second types of periodic orbits of the rotating Kepler problem can persist for all perturbed two-body and circular restricted three-body problems when the perturbation forces are conservative or the perturbed motion has its own extended Jacobian integral.
2023 - 10.3390/galaxies11020058
Galaxies, Vol. 11, Issue 2 (April 2023) , art. 58  
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23.
On the C1 non-integrability of the autonomous differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In the study of the dynamics of the autonomous differential systems to know the existence or non-existence of first integrals is a relevant fact. These last decades the meromorphic non-integrability of the autonomous differential systems have been studied intensively using the Ziglin's and the Morales-Ramis' theories. [...]
2023 - 10.1016/j.nonrwa.2023.103943
Nonlinear Analysis: Real World Applications, Vol. 74 (December 2023) , art. 103943  
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24.
Invariants of polynomial vector fields / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We characterize the existence of first integrals and invariants (first integrals depending on the time) for the polynomial vector fields which are invariant under an involution.
2023 - 10.1016/j.jde.2023.05.024
Journal of differential equations, Vol. 365 (August 2023) , p. 895-904  
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25.
On the "traveling pulses" of the limit of the FitzHugh-Nagumo equation when ɛ→0 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
A solution (u(s), v(s)) of the differential system u = v, v = −cv−u(u−a)(1−u) + w, w = −(ɛ/c)(u−γw) with a, c, ɛ ∈ R such that (u(s), v(s)) → (0,0) when s → ± ∞ is a traveling pulse of the FitzHugh-Nagumo equation. [...]
2023 - 10.1016/j.nonrwa.2023.103891
Nonlinear Analysis: Real World Applications, Vol. 73 (October 2023) , art. 103891  
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26.
981.0 KB Contributions to the study of periodic orbits and invariant manifolds in dynamical systems / Cufí Cabré, Clara ; Fontich, Ernest, 1955-, dir. ; Llibre, Jaume, dir. ; Gasull i Embid, Armengol, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
Aquesta tesi tracta l'estudi de varietats invariants i òrbites periòdiques de sistemes dinàmics discrets i continus. La memòria està dividida en dues parts que es poden llegir de manera independent. [...]
Esta tesis trata sobre el estudio de variedades invariantes y órbitas periódicas de sistemas dinámicos discretos y continuos. La memoria se divide en dos partes que se pueden leer de forma independiente. [...]
This thesis concerns the study of invariant manifolds and periodic orbits of discrete and continuous dynamical systems. The memoir is divided into two parts that can be read independently. The first part (Chapters 1-6) is dedicated to the study of invariant manifolds associated with parabolic points and parabolic invariant tori. [...]
2023  
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27.
19 p, 397.7 KB Limit Cycles of Polynomially Integrable Piecewise Differential Systems / García, Belén (Universidad de Oviedo. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez del Río, Jesús S. (Universidad de Oviedo. Departamento de Matemáticas) ; Pérez-González, Set (Universidad de Oviedo. Departamento de Matemáticas)
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. [...]
2023 - 10.3390/axioms12040342
Axioms, Vol. 12, Issue 4 (March 2023) , art. 342  
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28.
11 p, 301.0 KB Periodic Orbits of Quantised Restricted Three-Body Problem / Abouelmagd, Elbaz I. (National Research Institute of Astronomy and Geophysics . Astronomy Department) ; Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, perturbed third-body motion is considered under quantum corrections to analyse the existence of periodic orbits. These orbits are studied through two approaches to identify the first (second) periodic-orbit types. [...]
2023 - 10.3390/universe9030149
Universe, Vol. 9, Issue 3 (March 2023) , art. 149  
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29.
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)  
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30.
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  
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UAB Digital Repository of Documents : 785 records found   beginprevious21 - 30nextend  jump to record:
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