PermalinkSubmitted by jeromebuzzi on Wed, 08/02/2017 - 00:11

Dropping the expanding condition (which cannot be satisfied on the interval), on the set of continuous interval maps, the topological entropy is lower-semicontinuous but not upper-semicontinuous [1]. It is continuous among $C^\infty$ interval maps, as a consequence of Yomdin's theory [2].

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## On the set of continuous

Dropping the expanding condition (which cannot be satisfied on the interval), on the set of continuous interval maps, the topological entropy is lower-semicontinuous but not upper-semicontinuous [1]. It is continuous among $C^\infty$ interval maps, as a consequence of Yomdin's theory [2].

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