Abstract
We study the behavior of time-periodic three-dimensionalincompressible flows modelled by three-dimensionalvolume-preserving maps in the presence of a leakage. Thedistribution of residence times, and the chaotic saddle togetherwith its stable and unstable invariant manifolds are describedand characterized. They shed light on typical filamentation ofchaotic flows whose local stable and unstable manifolds arealways of different character (plane or line). We point out thatleaking is a useful method which sheds light on typicalfilamentation of chaotic flows. In particular, the topologydepends on the number of local expanding directions, and is thesame in the leaked system as in the closed flow.
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