On the Integrability of Liénard systems with a strong saddle

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2017
Author
Giné, Jaume
Llibre, Jaume
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Abstract
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.
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http://hdl.handle.net/10459.1/62956
DOI
https://doi.org/10.1016/j.aml.2017.03.004
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Applied Mathematics Letters, 2017, vol. 70, p. 39-45
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cc-by-nc-nd (c) Elsevier, 2017
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2017