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Título:
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On the Integrability of Liénard systems with a strong saddle
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Autor/a:
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Giné, Jaume; Llibre, Jaume
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Notas:
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We study the local analytic integrability for real Li\'{e}nard systems, $\dot x=y-F(x),$ $\dot y= x$, with $F(0)=0$ but $F'(0)\ne0,$ which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the $[p:-q]$ resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the $[p:-q]$ resonant saddle into a strong saddle.
The first author is partially supported by a MINECO/FEDER grant number MTM2014-
53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR-1204. The
second author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a
MINEC0 grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568. |
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Materia(s):
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-Center problem
-Analytic integrability
-Strong saddle |
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Derechos:
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cc-by-nc-nd (c) Elsevier, 2017
http://creativecommons.org/licenses/by-nc-nd/3.0/es
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Tipo de documento:
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Artículo
Artículo - Versión aceptada |
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Editor:
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Elsevier
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Compartir:
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