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Título:
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Cyclicity of a class of polynomial nilpotent center singularities
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Autor/a:
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García, I. A. (Isaac A.); Shafer, Douglas S.
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Notas:
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In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + 1}(x,y)$, $\dot y = Q_{2m + 1}(x,y)$, where $P_{2m+1}$ and $Q_{2m+1}$ are homogeneous polynomials of degree $2m + 1$ in $x$ and $y$. We use the method to obtain an upper bound (which is sharp in this case) on the cyclicity of all centers in the cubic family and all centers in a broad subclass in the quintic family.
The first author is partially supported by a MICINN grant number MTM2011-22877 and by a CIRIT grant number 2014 SGR 1204. |
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Materia(s):
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-Cyclicity
-Limit cycle
-Nilpotent center
-Matemàtica
-Mathematics |
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Derechos:
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(c) American Institute of Mathematical Sciences, 2016
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Tipo de documento:
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Artículo
Artículo - Versión aceptada |
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Editor:
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American Institute of Mathematical Sciences
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Compartir:
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