Abstract
The existence of an invariant fractal tiling of phase space for unbound Hamiltonian systems is demonstrated. The fractal properties of this partitioning of phase space is intimately related to the redistribution of energy among the various modes of the system. The existence of this tiling enables one to express the expectation values of physical observables as infinite sums over all of the tiles. Furthermore, knowledge of the scaling laws associated with the tiling then enables one to evaluate these sums.
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