  We study finite state transduction of automatic and morphic sequences.
Dekking proved that morphic sequences are closed under transduction and in
particular morphic images. We present a simple proof of this fact, and use the
construction in the proof to show that non-erasing transductions preserve a
condition called alpha-substitutivity. Roughly, a sequence is
alpha-substitutive if the sequence can be obtained as the limit of iterating a
substitution with dominant eigenvalue alpha. Our results culminate in the
following fact: for multiplicatively independent real numbers alpha and beta,
if v is an alpha-substitutive sequence and w is a beta-substitutive sequence,
then v and w have no common non-erasing transducts except for the ultimately
periodic sequences. We rely on Cobham's theorem for substitutions, a recent
result of Durand.
