A Complex Gap Lemma

Abstract : Inspired by the work of Newhouse in one real variable, we introduce a relevant notion of thickness for dynamical Cantor sets of the plane associated to a holomorphic IFS. Our main result is a complex version of Newhouse's Gap Lemma : we show that under some assumptions, if the product t(K)t(L) of the thicknesses of two Cantor sets K and L is larger than 1, then K and L have non empty intersection. Since in addition this thickness varies continuously, this gives a criterion to get a robust intersection between two Cantor sets in the plane.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01887360
Contributeur : Sébastien Biebler <>
Soumis le : jeudi 4 octobre 2018 - 13:40:54
Dernière modification le : samedi 6 octobre 2018 - 01:04:08

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gp211.pdf
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  • HAL Id : hal-01887360, version 1
  • ARXIV : 1810.02544

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Sébastien Biebler. A Complex Gap Lemma. 2018. 〈hal-01887360〉

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