  We relate the properties of the postsingular set for the exponential family
to the questions of stability. We calculate the action of the Ruelle operator
for the exponential family. We prove that if the asymptotic value is a summable
point and its orbit satisfies certain topological conditions, the map is
unstable hence there are no Beltrami differentials in the Julia set. Also we
show that if the postsingular set is a compact set, then the singular value is
summable.
