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Artículos, Encontrados 15 registros
Artículos Encontrados 15 registros  1 - 10siguiente  ir al registro:
1.
34 p, 632.0 KB Asymptotic Development of an Integral Operator and Boundedness of the Criticality of Potential Centers / Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the period function of planar potential centers. [...]
2019 - 10.1007/s10884-019-09753-2
Journal of dynamics and differential equations, (April 2019)  
2.
7 p, 419.1 KB On the periods of a continuous self-map on a graph / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena (Múrcia). Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let G be a graph and f be a continuous self-map on G. We present new and known results (from another point of view) on the periods of the periodic orbits of f using mainly the action of f on its homology, or the shape of the graph G.
2019 - 10.1007/s40314-019-0846-0
Computational & applied mathematics, Vol. 38, Issue 2 (June 2019) , art. 78  
3.
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  
4.
19 p, 504.7 KB Study of the period function of a two-parameter family of centers / 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 study the period function of ẍ = (1 x) p − (1 x) q , with p, q ∈ R and p > q. We prove three independent results. The first one establishes some regions in the parameter space where the corresponding center has a monotonous period function. [...]
2017 - 10.1016/j.jmaa.2017.02.054
Journal of Mathematical Analysis and Applications, Vol. 452 (2017) , p. 188-208  
5.
18 p, 330.6 KB Global behaviour of the period function for some degenerate centers / Álvarez, Maria Jesús (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica)
We study the global behaviour of the period function on the period annulus of degenerate centers for two families of planar polynomial vector fields. These families are the quasi-homogeneous vector fields and the vector fields given by the sum of two quasi-homogeneous Hamiltonian ones. [...]
2017 - 10.1016/j.jmaa.2016.12.077
Journal of Mathematical Analysis and Applications, Vol. 449 Núm. 2 (2017) , p. 1553-1569  
6.
41 p, 612.7 KB The criticality of centers of potential systems at the outer boundary / 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)
The number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied. We call this number the criticality at the outer boundary. Our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1. [...]
2016 - 10.1016/j.jde.2015.11.040
Journal of Differential Equations, Vol. 260 (2016) , p. 4918-4972  
7.
21 p, 2.2 MB Unfolding of saddle-nodes and their Dulac time / Mardesic, Pavao (Université de Bourgogne. Institut de Mathématiques de Bourgogne) ; Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Saavedra, M. (Universidad de Concepción. Departamento de Matemáticas) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. [...]
2016 - 10.1016/j.jde.2016.08.040
Journal of differential equations, Vol. 261, issue 11 (Dec. 2016) , p. 6411–6436  
8.
14 p, 608.8 KB Periodic solutions for nonlinear differential systems: The second order bifurcation function / Buica, Adriana (Babes-Bolyai University(Romania). Department of Mathematics) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We are concerned here with the classical problem of Poincaré of persistence of periodic solutions under small perturbations. The main contribution of this work is to give the expression of the second order bifurcation function in more general hypotheses than the ones already existing in the literature. [...]
2014
Topological Methods in Nonlinear Analysis, Vol. 43 Núm. 2 (2014) , p. 403-419  
9.
18 p, 451.0 KB Algebraic and analytical tools for the study of the period function / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Villadelprat, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
In this paper we consider analytic planar differential systems having a first integral of the form H(x, y) = A(x) + B(x)y + C(x)y2 and an integrating factor κ(x) not depending on y. Our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results. [...]
2014 - 10.1016/j.jde.2014.05.044
Journal of Differential Equations, Vol. 254 (2014) , p. 2464-2484  
10.
7 p, 2.1 MB Periodic structure of transversal maps on CP^n, HP^n and S^p S^q / Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
A C1 map f : M → M is called transversal if for all m ∈ N the graph of fm intersects transversally the diagonal of M × M at each point (x, x) being x a fixed point of fm. Let CPn be the n–dimensional complex projective space, HPn be the n–dimensional quaternion projective space and Sp × Sq be the product space of the p–dimensional with the q–dimensional spheres, p 6= q. [...]
2013 - 10.1007/s12346-013-0099-z
Qualitative Theory of Dynamical Systems, Vol. 12 (2013) , p. 417-425  

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