Opening up Fractal Structures of Three Dimensional Flows via Leaking

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). A possible application to magma flows
is discussed.