RIGIDITY OF JULIA SETS FOR HENON TYPE MAPS

被引：20

作者：

Tien-Cuong Dinh ^{[1
]}

Sibony, Nessim ^{[2
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[2] Univ Paris 11, Math, F-91405 Orsay, France

来源：

JOURNAL OF MODERN DYNAMICS | 2014年 / 8卷 / 3-4期

关键词：

Henon map; holomorphic automorphism; Julia set; Green current; Nevanlinna theory; rigidity; RIEMANN BILINEAR RELATIONS; POLYNOMIAL DIFFEOMORPHISMS; INTERSECTION THEORY; HARMONIC CURRENTS; SUPER-POTENTIALS; AUTOMORPHISMS; DYNAMICS; ERGODICITY; MAPPINGS; ENTROPY;

D O I：

10.3934/jmd.2014.8.499

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the Julia set of a Henon type automorphism on C-2 is very rigid: it supports a unique positive dd(c)-closed current of mass 1. A similar property holds for the cohomology class of the Green current associated with an automorphism of positive entropy on a compact Kahler surface. Relations between this phenomenon, several quantitative equidistribution properties and the theory of value distribution will be discussed. We also survey some rigidity properties of Henon type maps on C-k and of automorphisms of compact Kahler manifolds.

引用

页码：499 / 548

页数：50

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