Almost periodic homeomorphism flow conjecture

Let $M$ be a connected $n$-manifold. A homeomorphism $f$ of $M$ is almost periodic when the subgroup of $\operatorname{Homeo}(M)$ that it generates has compact closure. Almost periodic homeomorphism flow conjecture. For every almost periodic homeomorphism $f$ of $M$, there exists $r>0$ such that $f^r$ lies in the image of some homomorphism $\mathbb R\to\operatorname{Homeo}(M)$. This is stated as a consequence of the Hilbert–Smith conjecture for a fixed manifold, rather than as an independent conjecture. The supplied parser marks the underlying candidate disproved; the exact status of this consequence should be checked against the paper's argument.