Depósito Digital de Documentos de la UAB Encontrados 9 registros  La búsqueda tardó 0.02 segundos. 
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.
10 p, 362.5 KB A proof of Bertrand's theorem using the theory of isochronous potentials / Ortega, Rafael (Universidad de Granada. Departamento de Matemática Aplicada) ; Rojas, David (Universidad de Granada. Departamento de Matemática Aplicada)
We give an alternative proof for the celebrated Bertrand's theorem as a corollary of the isochronicity of a certain family of centers.
2018 - 10.1007/s10884-018-9676-9
Journal of dynamics and differential equations, Published online May 2018  
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.
15 p, 625.2 KB Centers and uniform isochronous centers of planar polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat de Barcelona) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
For planar polynomial vector fields of the form \[ (-y X(x,y)) x (x Y(x,y)) y, \] where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers.
2018 - 10.1007/s10884-018-9672-0
Journal of dynamics and differential equations, Vol. 30, issue 3 (Sep. 2018) , p. 1295-1310  
5.
52 p, 1.0 MB Inverse Approach in Ordinary Differential Equations: Applications to Lagrangian and Hamiltonian Mechanics / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
This paper is on the so called inverse problem of ordinary differential systems, i. e. the problem of determining the differential systems satisfying a set of given properties. More precisely, we characterize under very general assumptions the ordinary differential systems in RN which have a given set of either M ≤ N, or M > N partial integrals, or M < N first integrals, or M ≤ N partial and first integrals. [...]
2014 - 10.1007/s10884-014-9390-1
Journal of Dynamics and Differential Equations, Vol. 26 (2014) , p. 529-581  
6.
16 p, 384.2 KB Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in R^3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Rebollo-Perdomo, Salomón (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We consider the polynomial vector fields of arbitrary degree in R3 having the 2–dimensional algebraic torus T2(l, m, n) = {(x, y, z) ∈ R3: (x2l + y2m − r2)2 + z2n − 1 = 0}, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. [...]
2013 - 10.1007/s10884-013-9315-4
Journal of Dynamics and Differential Equations, Vol. 25 Núm. 3 (2013) , p. 777-793  
7.
14 p, 711.4 KB Synchronization and non-smooth dynamical systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; da Silva, Paulo Ricardo (IBILCE–UNESP(Brazil). Departamento de Matemática) ; Teixeira, Marco Antonio (IMECC–UNICAMP(Brazil))
In this article we establish an interaction between nonsmooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. [...]
2012 - 10.1007/s10884-012-9239-4
Journal of Dynamics and Differential Equations, Vol. 24 (2012) , p. 1-12  
8.
20 p, 347.7 KB Planar vector fields with a given set of orbits / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
We determine all the C 1 planar vector fields with a given set of orbits of the form y − y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. [...]
2011 - 10.1007/s10884-011-9219-0
Journal of Dynamics and Differential Equations, Vol. 23 Núm. 4 (2011) , p. 885-902  
9.
13 p, 611.4 KB The co-circular central configurations of the 5 body problem / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n = 3. [...]
2015 - 10.1007/s10884-015-9429-y
Journal of Dynamics and Differential Equations, Vol. 27 (2015) , p. 55-67  

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