  Let $f : M \rightarrow M$ be a Morse-Smale diffeomorphism defined on a
compact and connected manifold without boundary. Let $C(M)$ denote the
hyperspace of all subcontinua of M endowed with the Hausdorff metric and $C(f)
: C(M) \rightarrow C(M)$ denote the induced homeomorphism of $f$. We show in
this paper that if $M$ is the unit circle $S^1$ then the induced map $C(f)$ has
not the shadowing property. Also we show that the topological entropy of $C(f)$
has only two possible values: $0$ or $\infty$. In particular, we show that the
entropy of $C(f)$ is $0$ when $M$ is the unit circle $S^1$ and it is $\infty$
if the dimension of the manifold $M$ is greater than two. Furthermore, we study
the recurrence of the induced maps $2^f$ and $C(f)$ and sufficient conditions
to obtain infinite topological entropy in the hyperspace.
