I have a relatively well behaved vector field and I can prove that all the nonwandering points along the flow are equilibria. Is this enough to disprove that there is no homoclinic and heteroclinic cycles? In this previous question, in the accepted answer it is claimed that "single homoclinic loop consists of non-wandering points". I am also looking for a proof/reference for this claim that according to the user is based on the $\lambda$-lemma. Therefore, if (in my case) all nonwandering points are equilibria, does this disprove the existence of homoclinic orbits? Is it also true for etheroclinic loops (heteroclinic orbits connecting multiple equilibria in a loop).
Some analysis could be probably found here and it seems like the fact it's not true in general?. Currently reading.