We show that for a $C^1$ residual subset of diffeomorphisms far away from tangency, every non-trivial chain recurrent class that is accumulated by sources ia a homoclinic class contains periodic points with index 1 and it's the Hausdorff limit of a family of sources.
Transitivity and homoclinic classes for singular-hyperbolic systems
Lyapunov stable chain recurrent classes
Homoclinic classes and finitude of attractors for vector fields on n-manifolds
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