Nonwandering sets of interval skew products

被引：3
|
作者：
Kleptsyn, V. [1 ]
Volk, D. [2 ,3 ]
机构：
[1] CNRS, Inst Rech Mathemat Rennes, IRMAR, UMR CNRS 6625, Paris, France
[2] Univ Roma Tor Vergata, Rome, Italy
[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 117901, Russia
来源：
NONLINEARITY | 2014年 / 27卷 / 07期
关键词：
skew product; interval; partial hyperbolicity; subshift of finite type; nonwandering set; attractor;
D O I：
10.1088/0951-7715/27/7/1595
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider a class of skew products over transitive subshifts of finite type with interval fibres. For a natural class of 1-parameter families we prove that for all but countably many parameter values the nonwandering set (in particular, the union of all attractors and repellers) has zero measure. As a consequence, the same holds for a residual subset of the space of skew products.
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页码：1595 / 1601
页数：7
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