Bruin, Henk and Hawkins, Jane (2001) Exactness and maximal automorphic factors of unimodal interval maps. Ergodic Theory and Dynamical Systems, 21 (4). pp. 1009-1034. ISSN 0143-3857. doi:10.1017/S0143385701001481. https://resolver.caltech.edu/CaltechAUTHORS:20111116-153420523
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Abstract
We study exactness and maximal automorphic factors of C^3 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 C^3 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 | |||||||||
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| Additional Information: | © 2001 Cambridge University Press. Received 18 June 1999 and accepted in revised form 14 March 2000. The authors would like to thank Gerhard Keller for useful remarks and corrections on an earlier version of this paper. | |||||||||
| Issue or Number: | 4 | |||||||||
| DOI: | 10.1017/S0143385701001481 | |||||||||
| Record Number: | CaltechAUTHORS:20111116-153420523 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20111116-153420523 | |||||||||
| Official Citation: | Exactness and maximal automorphic factors of unimodal interval maps HENK BRUIN and JANE HAWKINS Ergodic Theory and Dynamical Systems / Volume 21 / Issue 0, pp 1009 - 1034 2001 Cambridge University Press Published online: 06 August 2001 DOI:10.1017/S0143385701001481 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 27818 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 17 Nov 2011 00:00 | |||||||||
| Last Modified: | 09 Nov 2021 16:52 |
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