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Abstract

A hypothesis about the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape through an opening is proposed. Eigenfunctions with decay rate gamma are described by a classical measure that (i) is conditionally invariant with classical decay rate gamma and (ii) is uniformly distributed on sets with the same temporal distance to the quantum resolved chaotic saddle. This explains the localization of fast-decaying resonance eigenfunctions classically. It is found to occur in the phase-space region having the largest distance to the chaotic saddle. We discuss the dependence on the decay rate gamma and the semiclassical limit. The hypothesis is numerically demonstrated for the standard map.