© 2015 Elsevier Inc. We study planar polynomial differential equations that in complex coordinates write as z ˙=Az+Bzkz-l+Czmz-n. We prove that for each p∈N there are differential equations of this type having at least p limit cycles. Moreover, for the particular case z ˙=Az+Bz-+Czmz-n, which has homogeneous nonlinearities, we show examples with several limit cycles and give a condition that ensures uniqueness and hyperbolicity of the limit cycle.
- Abelian integrals
- Homogeneous nonlinearities
- Limit cycles
- Z<inf>q</inf>-equivariant symmetry