Stable intersections of conformal Cantor sets

被引：1

作者：

Araujo, Hugo ^{[1
]}

Moreira, Carlos Gustavo ^{[2
]}

机构：

[1] Univ Fed Ouro Preto, Dept Ciencias Exatas & Aplicadas, BR-35931008 Joao Monlevade, MG, Brazil

[2] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, RJ, Brazil

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2023年 / 43卷 / 01期

关键词：

Cantor sets; smooth dynamics; bifurcation theory; symbolic dynamics; NEIGHBORHOODS; MAPS;

D O I：

10.1017/etds.2021.97

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate stable intersections of conformal Cantor sets and their consequences to dynamical systems. First we define this type of Cantor set and relate it to horseshoes appearing in automorphisms of C-2. Then we study limit geometries, that is, objects related to the asymptotic shape of the Cantor sets, to obtain a criterion that guarantees stable intersection between some configurations. Finally, we show that the Buzzard construction of a Newhouse region on Aut(C-2) can be seen as a case of stable intersection of Cantor sets in our sense and give some (not optimal) estimate on how 'thick' those sets have to be.

引用

页码：1 / 49

页数：49

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