Unicritical laminations

IF 0.5 3区 数学 Q3 MATHEMATICS
Sourav Bhattacharya, A. Blokh, D. Schleicher
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引用次数: 3

Abstract

. Thurston introduced invariant (quadratic) laminations in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polynomials. Important ingredients of his analysis of the angle doubling map σ 2 on the unit circle S 1 were the Central Strip Lemma, non-existence of wandering polygons, the transitivity of the first return map on vertices of periodic polygons, and the non-crossing of minors of quadratic invariant laminations. We use Thurston’s methods to prove similar results for unicritical laminations of arbitrary degree d and to show that the set of so-called minors of unicritical laminations themselves form a Unicritical Minor Lamination UML d . In the end we verify the Fatou conjecture for the unicritical laminations and extend the Lavaurs algorithm onto UML d .
Unicritical薄片
. Thurston在他1984年的预印本中引入了不变(二次)分层,作为理解连通Julia集合和二次多项式参数空间的工具。他分析单位圆s1上的翻角图σ 2的重要成分是中心条形引理、不存在游荡多边形、周期多边形顶点上的第一个返回图的可传递性以及二次不变层合的次元不交叉。我们使用Thurston的方法来证明任意度d的单临界层合的类似结果,并表明所谓的单临界层合的次要层合本身的集合形成了单临界小层合UML d。最后,我们验证了单临界分层的Fatou猜想,并将Lavaurs算法扩展到UML d上。
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来源期刊
Fundamenta Mathematicae
Fundamenta Mathematicae 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
44
审稿时长
6-12 weeks
期刊介绍: FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.
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