- We study the behavior of time-periodic three-dimensional incompressible flows modelled by three-dimensional volume-preserving maps in the presence of a leakage. The distribution of residence times, and the chaotic saddle together with its stable and unstable invariant manifolds are described and characterized. They shed light. on typical filamentation of chaotic flows whose local stable and unstable manifolds are always of different, character (plane or line). We point out that leaking is a useful method which sheds light on typical filamentation of chaotic flows. In particular; the topology depends on the number of local expanding directions, and is the same in the leaked system as in the closed flow
