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Title:
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Strongly formal Weierstrass non-integrability for polynomial differential systems in C2
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Author:
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Giné, Jaume; Llibre, Jaume
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Notes:
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Recently a criterion has been given for determining the weakly formal
Weierstrass non-integrability of polynomial differential systems in C2
. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability
which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2
. The criterion is based on the solutions of the form y = f(x) with
f(x) ∈ C[[x]] of the differential system whose integrability we are studying. The results
are applied to a differential system that contains the famous force-free Duffing and the
Duffing–Van der Pol oscillators.
The first author is partially supported by a MINECO/ FEDER grant number MTM2017-84383- P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR-1276. The second author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grant MTM2016-77278-P (FEDER) and grant MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911. |
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Subject(s):
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-Liouville integrability
-Weierstrass integrability
-Polynomial differential systems |
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Rights:
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cc-by (c) Giné, Jaume et al., 2020
http://creativecommons.org/licenses/by/4.0/
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Document type:
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Article
Article - Published version |
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Published by:
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Bolyai Institute, University of Szeged;
Hungarian Academy of Sciences
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