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
收藏
页码：381 / 414
页数：34
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