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Título:
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Integrability of Liénard systems with a weak saddle
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Autor/a:
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Gasull i Embid, Armengol; Giné, Jaume
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Notas:
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We characterize the local analytic integrability of weak saddles for complex Lienard systems, x˙ = y−F(x), y˙ = ax,
0 = a ∈ C, with F analytic at 0 and F(0) = F (0) = 0. We prove that they are locally integrable at the origin if and only if
F(x) is an even function. This result implies the well-known characterization of the centers for real Lienard systems. Our
proof is based on finding the obstructions for the existence of a formal integral at the complex saddle, by computing the
so-called resonant saddle quantities
The Armengol Gasull was supported by a MINECO Grant Number MTM2013-40998-P and by a CIRIT Grant Number 2014SGR568. The Jaume Gin´e was partially supported by a MINECO/ FEDER Grant Number MTM2014-53703-P and an AGAUR (Generalitat de Catalunya) Grant Number 2014SGR 1204. |
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Materia(s):
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-Center problem
-Analytic integrability
-Weak saddle
-Líenard equation |
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Derechos:
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(c) Springer International Publishing. 2016
info:eu-repo/semantics/restrictedAccess |
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Tipo de documento:
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article
publishedVersion |
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Editor:
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Springer International Publishing
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