A robustly chain transitive attractor with singularities of different indices. (English) Zbl 1304.37002
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.
Reviewer: Sergei Yu. Pilyugin (St. Petersburg)
MSC:
| 37-02 | Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory |
| 37D30 | Partially hyperbolic systems and dominated splittings |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37C29 | Homoclinic and heteroclinic orbits for dynamical systems |
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