Periodic perturbations of quadratic planar polynomial vector fields
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| Format: | Artículo científico |
| Language: | en |
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Academia Brasileira de Ciências
2002
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| _version_ | 1866815450440007680 |
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| author | Marcelo Messias |
| author_facet | Marcelo Messias |
| contents | Periodic perturbations of quadratic planar polynomial vector fields Marcelo Messias Multidisciplinaria (Ciencias Naturales y Exactas) polynomial systems heteroclinic cycles periodic perturbations In this work are studied periodic perturbations, depending on two parameters, of quadratic planarpolynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joiningtwo saddle points at infinity. The global study envolving infinity is performed via the Poincarécompactification. The main result obtained states that for certain types of periodic perturbations,the perturbed system has quadratic heteroclinic tangencies and transverse intersections betweenthe local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, viathe Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbedsystem, in a finite part of the phase plane. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774201 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.74 |
| format | Artículo científico |
| id | redalyc_32774201 |
| language | en |
| publishDate | 2002 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Periodic perturbations of quadratic planar polynomial vector fields Marcelo Messias Multidisciplinaria (Ciencias Naturales y Exactas) polynomial systems heteroclinic cycles periodic perturbations Periodic perturbations of quadratic planar polynomial vector fields Marcelo Messias Multidisciplinaria (Ciencias Naturales y Exactas) polynomial systems heteroclinic cycles periodic perturbations In this work are studied periodic perturbations, depending on two parameters, of quadratic planarpolynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joiningtwo saddle points at infinity. The global study envolving infinity is performed via the Poincarécompactification. The main result obtained states that for certain types of periodic perturbations,the perturbed system has quadratic heteroclinic tangencies and transverse intersections betweenthe local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, viathe Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbedsystem, in a finite part of the phase plane. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774201 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.74 |
| title | Periodic perturbations of quadratic planar polynomial vector fields |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) polynomial systems heteroclinic cycles periodic perturbations |
| url | https://www.redalyc.org/articulo.oa?id=32774201 |