Limit cycles for a class of quintic Z(6)-equivariant systems without infinite critical points

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Alvarez, MJ (Author) Other; Labouriau, IS (Author) FCUP; Murza, AC (Author) Other

Journal

Title: Bulletin of the Belgian Mathematical Society - Simon Stevin

Vol. 21

Pages: 841-857

ISSN: 1370-1444

Publisher: Belgian Mathematical Society

Indexing

ISI Web of Knowledge - 2 Citations

ISI Web of Science

Scopus

SciELO - Scientific Electronic Library Online

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00A-5ND

Abstract (EN): We analyze the dynamics of a class of Z(6)-equivariant systems of the form (z) over dot = pz(2)(z) over bar +sz(3)(z) over bar (2)-(z) over bar (5), where z is complex, the time t is real, while p and s are complex parameters. This study is the natural continuation of a previous work (M.J. Alvarez, A. Gasull, R. Prohens, Proc. Am. Math. Soc. 136, (2008), 1035-1043) on the normal form of Z(4)-equivariant systems. Our study uses the reduction of the equation to an Abel one, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17