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Exactness and maximal automorphic factors of unimodal interval maps

Bruin, Henk and Hawkins, Jane (2001) Exactness and maximal automorphic factors of unimodal interval maps Dynamical Systems, 21. pp. 1009-1034.

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Abstract

We study exactness and maximal automorphic factors of C3 unimodal maps of the interval. We show that for a large class of infinitely renormalizable maps, the maximal automorphic factor is an odometer with an ergodic non-singular measure. We give conditions under which maps with absorbing Cantor sets have an irrational rotation on a circle as a maximal automorphic factor, as well as giving exact examples of this type. We also prove that every C3 S-unimodal map with no attractor is exact with respect to Lebesgue measure. Additional results about measurable attractors in locally compact metric spaces are given.

Item Type: Article
Additional Information: Published in Ergodic Theory and Dynamical Systems, 21, 1009-1034. © 2001 Cambridge University Press. Reprinted with permission.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1434

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