Let $M$ be a smooth manifold, let $f: M \to M$ be a diffeomorphism, and let $\Lambda \subset M$ be an $f$-invariant Smale horseshoe. Suppose that there exists an integer $m \geq 2$ such that $f|_\Lambda$ is topologically conjugate to the full two-sided shift on the alphabet $A_m := \{1,\dots,m\}$. That is, if $\Sigma_m := A_m^{\mathbb{Z}}$ and $\sigma: \Sigma_m \to \Sigma_m$ is the shift map defined by $(\sigma s)_k = s_{k+1}$, then there is a homeomorphism $h: \Sigma_m \to \Lambda$ such that $h \circ \sigma = f|_\Lambda \circ h$.

Then for every $n \in \mathbb{N}$, the restriction $f|_\Lambda$ has a periodic orbit of least period $n$. More precisely, the periodic orbits of $f|_\Lambda$ of least period $n$ are in bijection with primitive words in the alphabet $A_m$ of length $n$, modulo cyclic permutation.