  For a continuous self-map $T$ of a compact metrizable space with finite
topological entropy, the order of accumulation of entropy of $T$ is a countable
ordinal that arises in the theory of entropy structure and symbolic extensions.
Given any compact manifold $M$ and any countable ordinal $\al$, we construct a
continuous, surjective self-map of $M$ having order of accumulation of entropy
$\al$. If the dimension of $M$ is at least 2, then the map can be chosen to be
a homeomorphism.
