Escaping Fatou components with disjoint hyperbolic limit sets

IF 1 3区 数学 Q1 MATHEMATICS
Veronica Beltrami, Anna Miriam Benini, Alberto Saracco
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引用次数: 0

Abstract

We construct automorphisms of \({{\mathbb {C}}}^2\) of constant Jacobian with a cycle of escaping Fatou components, on which there are exactly two limit functions, both of rank 1. On each such Fatou component, the limit sets for these limit functions are two disjoint hyperbolic subsets of the line at infinity. In the literature there are currently very few examples of automorphisms of \({{\mathbb {C}}}^2\) with rank one limit sets on the boundary of Fatou components. To our knowledge, this is the first example in which such limit sets are hyperbolic, and moreover different limit sets of rank 1 coexist.

Abstract Image

用互不相交的双曲极限集逃离法图成分
我们构造了雅各布常数的 \({{\mathbb {C}}^2\) 的自形体,其上有一个循环的逸出法图成分,在这些成分上恰好有两个极限函数,它们的秩都是 1。在每个这样的法图分量上,这些极限函数的极限集都是无穷远处直线的两个互不相交的双曲子集。在文献中,目前很少有例子表明 \({{\mathbb {C}}^2\) 的自形体在法图成分的边界上具有秩为 1 的极限集。据我们所知,这是第一个这种极限集是双曲的例子,而且不同秩 1 的极限集并存。
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
236
审稿时长
3-6 weeks
期刊介绍: "Mathematische Zeitschrift" is devoted to pure and applied mathematics. Reviews, problems etc. will not be published.
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