  A minimal Cantor system is said to be self-induced whenever it is conjugate
to one of its induced systems. Substitution subshifts and some odometers are
classical examples, and we show that these are the only examples in the
equicontinuous or expansive case. Nevertheless, we exhibit a zero entropy
self-induced system that is neither equicontinuous nor expansive. We also
provide non-uniquely ergodic self-induced systems with infinite
entropy.Moreover, we give a characterization of self-induced minimal Cantor
systems in terms of substitutions on finite or infinite alphabets.
