Resumen de Structural Stability of Planar Quasihomogeneous Vector Fields

Regilene Oliveira, Yulin Zhao

• Let Hpqm be the space of all planar (p, q)-quasihomogeneous vector fields of weight degreem endowed with the coefficient topology. In this paper we characterize the set pqm of all vector fields in Hpqm which are structurally stable with respect to perturbations in Hpqm in the Poincaré disc, and determine the exact number of the topological equivalence classes in pqm in terms of p, q and m. This characterization is applied to give an extension of the Hartman–Grobmann Theorem at the origin for (p, q) quasihomogeneous vector fields of weight degree greater than m starting with a term Xm ∈ pqm. This work is an extension of the Llibre et al.’s paper (J Differ Equ 125:490–520, 1996), where the homogeneous case was considered.