Polynomial vector fields in ℝ3 with infinitely many limit cycles

Antoni Ferragut; Jaume Llibre; Chara Pantazi

doi:https://doi.org/10.1142/S0218127413500296

Polynomial vector fields in ℝ³ with infinitely many limit cycles

Antoni Ferragut, Jaume Llibre, Chara Pantazi

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

We provide a constructive method to obtain polynomial vector fields in ℝ3 having infinitely many limit cycles starting from polynomial vector fields in ℝ2 with a period annulus. We present two examples of polynomial vector fields in ℝ3 having infinitely many limit cycles, one of them of degree 2 and the other one of degree 12. The main tools of our method are the Melnikov integral and the Hamiltonian structure. © 2013 World Scientific Publishing Company.

Original language	English
Article number	1350029
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	23
Issue number	2
DOIs	https://doi.org/10.1142/S0218127413500296
Publication status	Published - 1 Jan 2013

Keywords

Limit cycle
Melnikov integral

Access to Document

https://doi.org/10.1142/S0218127413500296

https://ddd.uab.cat/record/150665

Cite this

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abstract = "We provide a constructive method to obtain polynomial vector fields in ℝ3 having infinitely many limit cycles starting from polynomial vector fields in ℝ2 with a period annulus. We present two examples of polynomial vector fields in ℝ3 having infinitely many limit cycles, one of them of degree 2 and the other one of degree 12. The main tools of our method are the Melnikov integral and the Hamiltonian structure. {\textcopyright} 2013 World Scientific Publishing Company.",

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AU - Llibre, Jaume

AU - Pantazi, Chara

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AB - We provide a constructive method to obtain polynomial vector fields in ℝ3 having infinitely many limit cycles starting from polynomial vector fields in ℝ2 with a period annulus. We present two examples of polynomial vector fields in ℝ3 having infinitely many limit cycles, one of them of degree 2 and the other one of degree 12. The main tools of our method are the Melnikov integral and the Hamiltonian structure. © 2013 World Scientific Publishing Company.

KW - Limit cycle

KW - Melnikov integral

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