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Existence of periodic orbits for singular-hyperbolic sets. (English) Zbl 1124.37021

Every singular-hyperbolic attracting set of a \(C^1\) flow on a compact 3-manifold has a periodic orbit.

MSC:

37D30 Partially hyperbolic systems and dominated splittings
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C27 Periodic orbits of vector fields and flows
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