  We present an experiment that systematically probes the basins of attraction
of two fixed points of a nonlinear nanomechanical resonator and maps them out
with high resolution. We observe a separatrix which progressively alters shape
for varying drive strength and changes the relative areas of the two basins of
attraction. The observed separatrix is blurred due to ambient fluctuations,
including residual noise in the drive system, which cause uncertainty in the
preparation of an initial state close to the separatrix. We find a good
agreement between the experimentally mapped and theoretically calculated basins
of attraction.
