Large amplitude oscillations for a class of symmetric polynomial differential systems in R3
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2007
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| _version_ | 1876435886140293120 |
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| author | Jaume Llibre |
| author_facet | Jaume Llibre |
| contents | Large amplitude oscillations for a class of symmetric polynomial differential systems in R3 Jaume Llibre Marcelo Messias Multidisciplinaria (Ciencias Naturales y Exactas) periodic orbits symmetric systems infinite heteroclinic loops In this paper we study a class of symmetric polynomial differential systems in R3, which has a set of parallelinvariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints atinfinity. The global study near infinity is performed using the Poincaré compactification. We prove that forall n ∈ N there is εn > 0 such that for 0 < ε < εn the system has at least n large amplitude periodic orbitsbifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, onecontained in the half-space y > 0 and the other in y < 0. 2007 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32779401 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.4 Vol.79 |
| format | Artículo científico |
| id | redalyc_32779401 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Large amplitude oscillations for a class of symmetric polynomial differential systems in R3 Jaume Llibre Multidisciplinaria (Ciencias Naturales y Exactas) periodic orbits symmetric systems infinite heteroclinic loops Large amplitude oscillations for a class of symmetric polynomial differential systems in R3 Jaume Llibre Marcelo Messias Multidisciplinaria (Ciencias Naturales y Exactas) periodic orbits symmetric systems infinite heteroclinic loops In this paper we study a class of symmetric polynomial differential systems in R3, which has a set of parallelinvariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints atinfinity. The global study near infinity is performed using the Poincaré compactification. We prove that forall n ∈ N there is εn > 0 such that for 0 < ε < εn the system has at least n large amplitude periodic orbitsbifurcating from the heteroclinic loop formed by the two invariant straight lines closest to the x-axis, onecontained in the half-space y > 0 and the other in y < 0. 2007 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32779401 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.4 Vol.79 |
| title | Large amplitude oscillations for a class of symmetric polynomial differential systems in R3 |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) periodic orbits symmetric systems infinite heteroclinic loops |
| url | https://www.redalyc.org/articulo.oa?id=32779401 |