Non-smooth quadratic centers defined in two arbitrary sectors

Abstract

In this paper we analyze the center-focus problem of some families of piecewise planar quadratic vector fields on two zones of R2. The zones we consider are two unbounded sectors defined by an arbitrary angle α and a fixed vertex. We also assume that each vector field share a common weak focus singularity at the vertex of the boundary. We observe how the center variety depends on the angle α.

The author is partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204.