Abstract
In 1980, Yano showed that on smooth compact manifolds, for endomorphisms in dimension one or above and homeomorphisms in dimensions greater than one, topological entropy is generically infinite. It had earlier been shown that, for Lipschitz endomorphisms on such spaces, topological entropy is always finite. In this article, we investigate what occurs between C0-regularity and Lipschitz regularity, focussing on two cases: Hölder mappings and Sobolev mappings.
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