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Articles 18 records found  1 - 10next  jump to record:
1.
22 p, 816.7 KB Period function of planar turning points / Huzak, Renato (Hasselt University. Campus Diepenbeek (Belgium)) ; Rojas, David (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)
This paper is devoted to the study of the period function of planar generic and non-generic turning points. In the generic case (resp. non-generic) a non-degenerate (resp. degenerate) center disappears in the limit ɛ → 0, where ɛ ≥ 0 is the singular perturbation parameter. [...]
2021 - 10.14232/ejqtde.2021.1.16
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2021, Issue 16 (2021) , p. 1-21
2 documents
2.
Bifurcations of zeros in translated families of functions and applications / Mardešić, Pavao (Université de Bourgogne Franche-Comté. UFR Sciences et Techniques. Institut de Mathématiques de Bourgogne (France)) ; Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
In this paper, we study the creation of zeros in a certain type of families of functions. The families studied are given by the difference of two basic functions with a translation made in the argument of one of these functions. [...]
2020 - 10.1007/s10883-020-09520-3
Journal of Dynamical and Control Systems, (November 2020)  
3.
Criticality via first order development of the period constants / Sánchez-Sánchez, Iván (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the criticality of some planar systems of polynomial differential equations having a center for various low degrees n. To this end, we present a method which is equivalent to the use of the first non-identically zero Melnikov function in the problem of limit cycles bifurcation, but adapted to the period function. [...]
2021 - 10.1016/j.na.2020.112164
Nonlinear Analysis : Theory, Methods and Applications, Vol. 203 (February 2021) , art. 112164  
4.
12 p, 630.6 KB On the period function in a class of generalized Lotka-Volterra systems / Villadelprat Yagüe, Jordi (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
In this note, motivated by the recent results of Wang et al. [Wang et al. , Local bifurcations of critical periods in a generalized 2D LV system, Appl. Math. Comput. 214 (2009) 17-25], we study the behaviour of the period function of the center at the point (1,1) of the planar differential system {u' = up(1−vq),v'= μvq(up−1), where p, q, μ ∈ R with pq > 0 and μ > 0. [...]
2010 - 10.1016/j.amc.2010.03.025
Applied Mathematics and Computation, Vol. 216, Issue 7 (June 2010) , p. 1956-1964  
5.
19 p, 499.4 KB Bifurcation of critical periods from Pleshkan's isochrones / Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Pleshkan proved in 1969 that, up to a linear transformation and a constant rescaling of time, there are four isochrones in the family of cubic centers with homogeneous nonlinearities ℓ3. In this paper we prove that if we perturb any of these isochrones inside ℓ3, then at most two critical periods bifurcate from its period annulus. [...]
2010 - 10.1112/jlms/jdp062
Journal of the London Mathematical Society, Vol. 81, Issue 1 (February 2010) , p. 142-160  
6.
9 p, 634.4 KB A note on the Lyapunov and period constants / Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin of a weak focus or a non degenerated center for a family of planar polynomial vector fields is governed by the structure of the so called Lyapunov constants, that are polynomials in the parameters of the system. [...]
2020 - 10.1007/s12346-020-00375-4
Qualitative Theory of Dynamical Systems, Vol. 19, Issue 1 (April 2020) , art. 44  
7.
The period function of Hamiltonian systems with separable variables / Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences (China))
In this paper we study the period function of those planar Hamiltonian differential systems for which the Hamiltonian function H(x, y) has separable variables, i. e. , it can be written as H(x, y) = F1(x) + F2(y). [...]
2020 - 10.1007/s10884-019-09759-w
Journal of dynamics and differential equations, Vol. 32, Issue 2 (June 2020) , p. 741-767  
8.
On the upper bound of the criticality of potential systems at the outer boundary using the Roussarie-Ecalle compensator / Rojas, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This paper is concerned with the study of the criticality of families of planar centers. More precisely, we study sufficient conditions to bound the number of critical periodic orbits that bifurcate from the outer boundary of the period annulus of potential centers. [...]
2019 - 10.1016/j.jde.2019.04.021
Journal of differential equations, Vol. 267, Issue 6 (September 2019) , p. 3922-3951  
9.
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, Vol. 32, Issue 2 (June 2020) , p. 665-704  
10.
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 Yagüe, 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  

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