Hopf bifurcation at infinity and dissipative vector fields of the plane
This work deals with one-parameter families of differentiable planar vector fields for which the infinity reverses its stability as the parameter goes through zero. These vector fields are defined on the complement of some compact ball centered at the origin and have isolated singularities. They may be considered as linear perturbations at infinity of a vector field with some spectral property, for instance, dissipativity. We also address the case concerning linear perturbations of planar systems with a global period annulus. It is worth noting that the adopted approach is not restricted to consider vector fields which are strongly dominated by the linear part. Moreover, the Poincaré compactification is not applied in this paper.
Autor(es):RABANAL, R.
ALARCON, B.
Año: 2017
Título de la revista: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 145
Número: 7
Página inicial - Página final: 3033 -- 3046
ISSN: 1088-6826
Url: http://www.ams.org/journals/proc/2017-145-07/S0002-9939-2016-13462-X/