Orders of accumulation of entropy on manifolds

Kevin McGoff

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arXiv · 0912.1783

Orders of accumulation of entropy on manifolds

Kevin McGoff

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Abstract

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.

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Kevin McGoff. 2009-12-09. Orders of accumulation of entropy on manifolds. https://arxiv.org/abs/0912.1783

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