Results overview: Found 11 records in 0.03 seconds.
Articles, 10 records found
Research literature, 1 records found
Articles 10 records found  
1.
26 p, 414.4 KB New lower bounds for the Hilbert numbers using reversible centers / Prohens, Rafel (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we provide the best lower bounds, that are known up to now, for the Hilbert numbers of polynomial vector fields of degree N,, for small values of N. These limit cycles appear bifurcating from symmetric Darboux reversible centers with very high simultaneous cyclicity. [...]
2019 - 10.1088/1361-6544/aae94d
Nonlinearity, Vol. 32, Núm. 1 (January 2019) , p. 331-355  
2.
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  
3.
29 p, 488.3 KB Periodic orbits from second order perturbation via rational trigonometric integrals / Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The second order Poincaré-Pontryagin-Melnikov perturbation theory is used in this paper to study the number of bifurcated periodic orbits from certain centers. This approach also allows us to give the shape and the period up to first order. [...]
2014 - 10.1016/j.physd.2014.05.002
Physica D. Nonlinear Phenomena, Vol. 280-281 (2014) , p. 59-72  
4.
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  
5.
21 p, 638.6 KB Canard Trajectories in 3D piecewise linear systems / Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Teruel, Antonio E. (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
We present some results on singularly perturbed piecewise linear systems, similar to those obtained by the Geometric Singular Perturbation Theory. Unlike the differentiable case, in the piecewise linear case we obtain the global expression of the slow manifold Sε. [...]
2013 - 10.3934/dcds.2013.33.4595
Discrete and Continuous Dynamical Systems. Series A, Vol. 33 Núm. 10 (2013) , p. 4595-4611  
6.
2 p, 200.7 KB Corrigendum to "Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus" (Nonlinear Anal. 81 (2013) 130--148) / Prohens, Rafel (Universitat de les Illes Balears. Dept. de Matemàtiques i Informàtica) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In our paper [1] we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Actually, there is a mistake in the formula of the first order approximation of the period given in Corollary 4. [...]
2013 - 10.1016/j.na.2013.05.003
Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 93 (2013) , p. 1-2  
7.
20 p, 399.5 KB Alien limit cycles in Liénard equations / Coll, Bartomeu (Universitat de les Illes Balears. Dept. de Matemàtiques i Informàtica) ; Dumortier, Freddy (Universiteit Hasselt(Belgium). Dept. Wiskunde) ; Prohens, Rafel (Universitat de les Illes Balears. Dept. de Matemàtiques i Informàtica)
This paper aims at providing an example of a family of polynomial Liénard equations exhibiting an alien limit cycle. This limit cycle is perturbed from a 2-saddle cycle in the boundary of an annulus of periodic orbits given by a Hamiltonian vector field. [...]
2013 - 10.1016/j.jde.2012.11.005
Journal of Differential Equations, Vol. 254 (2013) , p. 1582-1600  
8.
23 p, 517.3 KB Limit Cycles for two families of cubic systems / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica)
In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of Volterra type. [...]
2012 - 10.1016/j.na.2012.07.012
Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, Vol. 75 (2012) , p. 6402-6417  
9.
17 p, 416.2 KB Periodic orbits for perturbed non-autonomous differential equations / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Matematiques i Informàtica) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Matematiques i Informàtica)
2012 - 10.1016/j.bulsci.2012.03.001
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 803-819  
10.
24 p, 438.8 KB Limit cycles bifurcating from a perturbed quartic center / Coll, Bartomeu (Universitat de les Illes Balears. Deptartament de Matemàtiques i Informàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Deptartament de Matemàtiques i Informàtica)
2011 - 10.1016/j.chaos.2011.02.009
Chaos, Solitons and Fractals, Vol. 44 (2011) , p. 317-334  

Research literature 1 records found  
1.
11 p, 144.2 KB Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points / Álvarez Torres, María Jesús ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens i Sastre, Rafel, J. ; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
"Vegeu el resum a l'inici del document del fitxer adjunt".
Centre de Recerca Matemàtica 2006 (Prepublicacions del Centre de Recerca Matemàtica ; 674)  

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