Existence of inverse integrating factors and Lie symmetries for degenerate planar centers

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Gine, Jaume²  Peralta-Salas, Daniel¹ 

[1] CSIC UAM UC3M UCM, Inst Ciencias Matemat, Madrid 28049, Spain

[2] Univ Lleida, Dept Matemat, Lleida 25001, Catalonia, Spain

关键词: Planar vector field;    Degenerate center;    Inverse integrating factor;    Lie symmetry;    First integral;   

DOI  :  10.1016/j.jde.2011.08.044

来源: Elsevier

【 摘 要 】

We prove that any (possibly degenerate) center of an analytic planar system admits a C(infinity) inverse integrating factor and a C(infinity) Lie symmetry in a neighborhood of the singularity. We also show that there exists an analytic degenerate center for which any C(infinity) inverse integrating factor is flat at the singular point, and that a sufficient condition for the existence of an analytic inverse integrating factor is the existence of an analytic first integral. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free