|
Title:
|
Integrability of Liénard systems with a weak saddle
|
|
Author:
|
Gasull i Embid, Armengol; Giné, Jaume
|
|
Notes:
|
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
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. |
|
Subject(s):
|
-Center problem
-Analytic integrability
-Weak saddle
-Líenard equation |
|
Rights:
|
(c) Springer International Publishing. 2016
info:eu-repo/semantics/restrictedAccess |
|
Document type:
|
article
publishedVersion |
|
Published by:
|
Springer International Publishing
|
|
Share:
|
|
