Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

Author(s)

Buzzi, Claudio A. ^[1] ; Llibre, Jaume ^[2] ; Medrado, Joao C. ^[3] ; Torregrosa, Joan ^[2]

Affiliation

^[1] IBILCE, UNESP, Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[3] Univ Fed Goias, Inst Matemat & Estat, Goiania, Go - Brazil

• Document type: Journal article
• Source: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 24, n. 1, p. 123-137, 2009.
• Web of Science Citations: 12

Abstract

For every positive integer N >= 2 we consider the linear differential centre (x) over dot = Ax in R(4) with eigenvalues +/- i and +/- Ni. We perturb this linear centre inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i.e. (x) over dot Ax + epsilon F(x) where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree N. Then if the displacement function of order epsilon of the perturbed system is not identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential centre. (AU)

• FAPESP's process: 07/04307-2 - Planar phase portraits and generic bifurcations of reversible vector fields
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Scholarships abroad - Research