  The effect of noise is studied in one-dimensional maps undergoing
transcritical, tangent, and pitchfork bifurcations. The attractors of the
noiseless map become metastable states in the presence of noise. In the
weak-noise limit, a symplectic two-dimensional map is associated with the
original one-dimensional map. The consequences of their noninvertibility on the
phase-space structures are discussed. Heteroclinic orbits are identified which
play a key role in the determination of the escape rates from the metastable
states. Near bifurcations, the critical slowing down justifies the use of a
continuous-time approximation replacing maps by flows, which allows the
analytic calculation of the escape rates. This method provides the universal
scaling behavior of the escape rates at the bifurcations.
