  Weak noise smooths out fractals in a chaotic state space and introduces a
maximum attainable resolution to its structure. The balance of noise and
deterministic stretching/contraction in each neighborhood introduces local
invariants of the dynamics that can be used to partition the state space. We
study the local discrete-time evolution of a density in a two-dimensional
hyperbolic state space, and use the asymptotic eigenfunctions for the noisy
dynamics to formulate a new state space partition algorithm.
