Tautness and Fatou Components in ℙ2

被引：0

作者：

Han Peters

Crystal Zeager

机构：

[1] Universiteit van Amsterdam,Korteweg de Vries Instituut voor Wiskunde

[2] University of Michigan,Mathematics Department

来源：

Journal of Geometric Analysis | 2012年 / 22卷

关键词：

Holomorphic dynamics; Fatou components; Kobayashi hyperbolicity; 32H50; 32F45;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Hyperbolicity played an important role in the classification of Fatou components for rational functions in the Riemann sphere. In higher dimensions Fatou components are not nearly as well understood. We investigate the Kobayashi completeness and tautness of invariant Fatou components for holomorphic endomorphisms of ℙ2 and for Hénon mappings. We show that basins of attraction and domains with an attracting Riemann surface, previously known to be taut, are also complete, which is strictly stronger. We also prove tautness for a class of Siegel domains.

引用

页码：934 / 941

页数：7

共 20 条

[1]

Abate M.(1991)Iteration theory compactly divergent sequences and commuting holomorphic maps Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 18 167-191

[2]

Barrett D.E.(1989)-actions on holomorphically separable complex manifolds Math. Z. 202 65-82

[3]

Bedford E.(1972)The Kobayashi distance induces the standard topology Proc. Am. Math. Soc. 35 439-441

[4]

Dadok J.(1983)On the automorphism group of a Stein manifold Math. Ann. 266 215-227

[5]

Barth T.J.(1926)Sur l’itération des fonctions analitiques C. R. Acad. Sci. 182 255-257

[6]

Bedford E.(1994)Complex dynamics in higher dimensions: 1, Complex analytic methods in dynamical systems (Rio de Janeiro, 1992) Astérisque 222 201-231

[7]

Denjoy A.(1995)Classification of recurrent domains for some holomorphic maps Math. Ann. 301 813-820

[8]

Fornæss J.E.(1994)Superattractive fixed points in ℂ Indiana Univ. Math. J. 43 321-365

[9]

Sibony N.(2003)Fatou maps in ℙ Int. J. Math. Math. Sci. 19 1233-1240

[10]

Fornæss J.E.(1994) dynamics J. Math. Soc. Jpn. 46 545-555

← 1 2 →