Existence of unique SRB-measures is typical for real unicritical polynomial families

被引：19

作者：

Bruin, Henk ^{[1
]}

Shen, Weixiao

Van Strien, Sebastian

机构：

[1] Univ Surrey, Guildford GU2 7XH, Surrey, England

[2] Univ Sci & Technol China, Dept Math, Anhua 230026, Peoples R China

[3] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2006年 / 39卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

D O I：

10.1016/j.ansens.2006.02.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that for a one-parameter family of unicritical polynomials {f(c)} with even critical order l >= 2, for almost all parameters c, f(c), admits a unique SRB-measure, being either absolutely continuous, or supported on the postcritical set. As a byproduct we prove that if f(c) has a Cantor attractor, then it is uniquely ergodic on its postcritical set. (c) 2006 Published by Elsevier Masson SAS.

引用

页码：381 / 414

页数：34

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