  All physical systems are affected by some noise that limits the resolution
that can be attained in partitioning their state space. For chaotic, locally
hyperbolic flows, this resolution depends on the interplay of the local
stretching/contraction and the smearing due to noise. We propose to determine
the `finest attainable' partition for a given hyperbolic dynamical system and a
given weak additive white noise, by computing the local eigenfunctions of the
adjoint Fokker-Planck operator along each periodic point, and using overlaps of
their widths as the criterion for an optimal partition. The Fokker-Planck
evolution is then represented by a finite transition graph, whose spectral
determinant yields time averages of dynamical observables. Numerical tests of
such `optimal partition' of a one-dimensional repeller support our hypothesis.
