Non wandering sets of interval skew products

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...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2014-07, Vol.27 (7), p.1595-1601
Main Authors: Kleptsyn, V, Volk, D
Format: Article
Language:English
Subjects:
Fibers
Fibres
Intervals
Mathematical analysis
Nonlinearity
Unions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/27/7/1595