On the structure of a neighborhood of an isolated equilibrium of a local planar dynamical system admiting the first approximation

We show that if all parabolic sectors in the space Z _∞ are stable, then neighborhoods of the point under study in the phase planes of the spaces Z and Z _∞ have the same structure; i.e., the number and order of sectors coincide. (Parabolic sectors may degenerate into a single trajectory.) If there is no hyperbolic sector in the space Z _∞, then the spaces Z and Z _∞ are isomorphic. We present examples showing that all conditions in these assertions are essential.