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On the Integrability of Liénard systems with a strong saddle
Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2017
Abstract: We study the local analytic integrability for real Li\'enard systems, x=y-F(x), y= x, with F(0)=0 but F'(0)0, 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.
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció AGAUR/2014/SGR-1204
Note: Número d'acord de subvenció MINECO/MTM2014-53703-P
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció MINECO/MTM2016-77278-P
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Analytic integrability ; Center problem ; Liénard equations ; Resonant saddle ; Strong saddle
Published in: Applied Mathematics Letters. An International Journal of Rapid Publication, Vol. 70 (2017) , p. 39-45, ISSN 0893-9659

DOI: 10.1016/j.aml.2017.03.004


preprint
7 p, 731.3 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2017-11-28, last modified 2019-02-02



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