ACCESSES TO INFINITY FROM FATOU COMPONENTS

被引：18

作者：

Baranski, Krzysztof ^{[1
]}

Fagella, Nuria ^{[2
,3
]}

Jarque, Xavier ^{[2
,3
]}

Karpinska, Boguslawa ^{[4
]}

机构：

[1] Univ Warsaw, Inst Math, Ul Banacha 2, PL-02097 Warsaw, Poland

[2] Univ Barcelona, Barcelona Grad Sch Math, E-08007 Barcelona, Catalonia, Spain

[3] Univ Barcelona, Dept Matemat & Informat, E-08007 Barcelona, Catalonia, Spain

[4] Warsaw Univ Technol, Fac Math & Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 03期

关键词：

MEROMORPHIC FUNCTIONS; NEWTONS METHOD; ATTRACTING BASINS; ENTIRE MAPS; BOUNDARIES; TREES;

D O I：

10.1090/tran/6739

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the boundary behaviour of a meromorphic map f : C -> (C) over cap on its simply connected invariant Fatou component U. To this aim, we develop the theory of accesses to boundary points of U and their relation to the dynamics of f. In particular, we establish a correspondence between invariant accesses from U to infinity or weakly repelling fixed points of f and boundary fixed points of the associated inner function on the unit disc. We apply our results to describe the accesses to infinity from invariant Fatou components of the Newton maps.

引用

页码：1835 / 1867

页数：33

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