Results overview: Found 6 records in 0.03 seconds.
Articles, 6 records found
Articles 6 records found  
1.
26 p, 687.0 KB Simultaneous bifurcation of limit cycles from a cubic piecewise center with two period annuli / Da Cruz, Leonardo Pereira Costa (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of periodic orbits that bifurcate from a cubic polynomial vector field having two period annuli via piecewise perturbations. The cubic planar system (x',y')= (-y((x-1)² + y²),x((x-1)² + y²) has simultaneously a center at the origin and at infinity. [...]
2018 - 10.1016/j.jmaa.2017.12.072
Journal of mathematical analysis and applications, Vol. 461, issue 1 (May 2018) , p. 248-272  
2.
26 p, 622.2 KB Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus / Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Fran¸coise develop a method to obtain the first non vanishing Poincaré-Pontryagin-Melnikov function. [...]
2013 - 10.1016/j.na.2012.10.017
Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 81 (2013) , p. 130-148  
3.
17 p, 629.0 KB A proof of Perko's conjectures for the Bogdanov-Takens system / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. [...]
2013 - 10.1016/j.jde.2013.07.006
Journal of Differential Equations, Vol. 255 (2013) , p. 2655-2671  
4.
11 p, 279.4 KB Limit cycles appearing from the perturbation of a system with a multiple line of critical points / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Consider the planar ordinary differential equation ˙x = −y(1 − y)m, y˙ = x(1 − y)m, where m is a positive integer number. We study the maximum number of zeroes of the Abelian integral M that controls the limit cycles that bifurcate from the period annulus of the origin when we perturb it with an arbitrary polynomial vector field. [...]
2012 - 10.1016/j.na.2011.08.032
Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 75 (2012) , p. 278-285  
5.
33 p, 1.1 MB Bifurcation values for a familiy of planar vector fields of degree five / García Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours (France). Laboratoire de Mathématiques et Physique Théorique)
We study the number of limit cycles and the bifurcation diagram in the Poincar' sphere of a one-parameter family of planar differential equations of degree e ˙ five x = Xb (x) which has been already considered in previous papers. [...]
2015 - 10.3934/dcds.2015.35.669
Discrete and Continuous Dynamical Systems. Series A, Vol. 35 Núm. 2 (2015) , p. 669-701  
6.
28 p, 438.5 KB Limit cycles bifurcating from planar polynomial quasi-homogeneous centers / Giné, Jaume (Universitat de Lleida. Departament de Matematica) ; Grau, Maite (Universitat de Lleida. Departament de Matematica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we find an upper bound for the maximum number of limit cycles bifurcating from the periodic orbits of any planar polynomial quasi-homogeneous center, which can be obtained using first order averaging method. [...]
2015 - 10.1016/j.jde.2015.08.014
Journal of Differential Equations, Vol. 259 (2015) , p. 7135-7160  

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