Translator Disclaimer
december 2014 Limit cycles for a class of quintic $\mathbb{Z}_6$-equivariant systems without infinite critical points
M.J. Àlvarez, I.S. Labouriau, A.C. Murza
Bull. Belg. Math. Soc. Simon Stevin 21(5): 841-857 (december 2014). DOI: 10.36045/bbms/1420071857

Abstract

We analyze the dynamics of a class of $\mathbb{Z}_6$-equivariant systems of the form $\dot{z}=pz^2\bar{z}+sz^3\bar{z}^2-\bar{z}^{5},$ 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. Àlvarez, A. Gasull, R. Prohens, Proc. Am. Math. Soc. \textbf{136}, (2008), 1035--1043) on the normal form of $\mathbb{Z}_4$-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.

Citation

Download Citation

M.J. Àlvarez. I.S. Labouriau. A.C. Murza. "Limit cycles for a class of quintic $\mathbb{Z}_6$-equivariant systems without infinite critical points." Bull. Belg. Math. Soc. Simon Stevin 21 (5) 841 - 857, december 2014. https://doi.org/10.36045/bbms/1420071857

Information

Published: december 2014
First available in Project Euclid: 1 January 2015

zbMATH: 1308.34039
MathSciNet: MR3298481
Digital Object Identifier: 10.36045/bbms/1420071857

Subjects:
Primary: 34C07, 34C14
Secondary: 34C23, 37C27

Rights: Copyright © 2014 The Belgian Mathematical Society

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.21 • No. 5 • december 2014
Back to Top