On the minimality of semigroup actions on the interval which are C¹-close to the identity
classification
🧮 math.DS
keywords
intervalactionscloseidentitysemigrouparticleattractingcoincides
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We consider semigroup actions on the interval generated by two attracting maps. It is known that if the generators are sufficiently $C^2$-close to the identity, then the minimal set coincides with the whole interval. In this article, we give a counterexample to this result under the $C^1$-topology.
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