Let $f:M \to M$ be a $C^r$ diffeomorphism, $r \ge 1$, of a smooth surface, and let $p$ be a hyperbolic periodic point. If $p$ has a transverse homoclinic point, then there exists $m \in \mathbb N$ and a compact $f^m$-invariant hyperbolic set $\Lambda \subset M$ near the homoclinic orbit such that $f^m|_{\Lambda}$ is topologically conjugate to a subshift of finite type. In particular, after restricting to a suitable invariant subset, the dynamics contains a full shift on two symbols.