Cyclicity of Infinite Contour around Certain Reversible Quadratic Center

The paper deals with quadratic vector fields on the Poincairé sphere with center of the reversible kind.x=y(1−2x),y=−x+ay2+bx2. In this case there is a 2-cycle with hyperbolic vertices at infinity. We show that the cyclicity of this 2-cycle is 2 or 3. The last possibility takes place along some curve in the (a, b) plane.