A robustly chain transitive attractor with singularities of different indices (Q2841758)

The authors construct a \(C^1\)-open set in the space of smooth vector fields on a 4-manifold with the \(C^1\)-topology such that any vector field in this set has a robustly chain transitive attractor containing two hyperbolic rest points of different indices. It is also shown that, for any robust attractor having such properties, \(C^1\)-small perturbations create homoclinic tangencies and heterodimensional cycles associated to closed orbits belonging to the attractor.