POLYNOMIAL VECTOR FIELDS IN ℝ3 WITH INFINITELY MANY LIMIT CYCLES-Reference-Cited by-同舟云学术

POLYNOMIAL VECTOR FIELDS IN ℝ3 WITH INFINITELY MANY LIMIT CYCLES

Published:2013-02 Issue:02 Volume:23 Page:1350029
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

FERRAGUT ANTONI¹,LLIBRE JAUME²,PANTAZI CHARA³

Affiliation:

1. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028, Barcelona, Catalonia, Spain

2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Catalonia, Spain

3. Departament de Matemàtica Aplicada I (EPSEB), Universitat Politècnica de Catalunya, Av. Doctor Marañón, 44-50, Barcelona, Catalonia, Spain

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127413500296

Reference14 articles.

1. An extension of Poincaré's last geometric theorem

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