dc.contributor.author |
Gasull i Embid, Armengol |
dc.contributor.author |
Giné, Jaume |
dc.date |
2017-01-20T10:59:05Z |
dc.date |
2017 |
dc.date |
10000-01-01 |
dc.identifier |
0044-2275 |
dc.identifier |
http://hdl.handle.net/10459.1/59059 |
dc.identifier |
https://doi.org/10.1007/s00033-016-0756-6 |
dc.identifier.uri |
http://hdl.handle.net/10459.1/59059 |
dc.description |
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 |
dc.description |
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. |
dc.language |
eng |
dc.publisher |
Springer International Publishing |
dc.relation |
MINECO/PN2013-2016/MTM2013-40998-P |
dc.relation |
MINECO/PN2013-2016/MTM2014-53703-P |
dc.relation |
Reproducció del document publicat a https://doi.org/10.1007/s00033-016-0756-6 |
dc.relation |
Zeitschrift für angewandte Mathematik und Physik, 2017, vol. 68, núm. 13, p 1-13 |
dc.rights |
(c) Springer International Publishing. 2016 |
dc.rights |
info:eu-repo/semantics/restrictedAccess |
dc.subject |
Center problem |
dc.subject |
Analytic integrability |
dc.subject |
Weak saddle |
dc.subject |
Líenard equation |
dc.title |
Integrability of Liénard systems with a weak saddle |
dc.type |
article |
dc.type |
publishedVersion |