This article analyzes the continuum-mechanical representation of the global
invariant geometric properties of 2D time-periodic Hamiltonian systems and
chaotic flows. An application of this analysis concerns the evolution in t
ime of the invariant measure associated with the space-filling properties o
f the invariant unstable foliation related in laminar chaotic flows to the
pointwise intermaterial contact-area density between fluid elements. (C) 19
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