  We analyze the dynamics of a 4-parameter family of planar ordinary
differential equations, given by a polynomial of degree 5 that is equivariant
under a symmetry of order 6. We obtain the number of limit cycles as a function
of the parameters, and provide criteria for proving in some cases uniqueness
and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical
points, the origin being always one of these points. The method used is the
reduction of the problem to an Abel equation.
