Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bruin, Henk and Todd, Mike 2015. Wild attractors and thermodynamic formalism. Monatshefte für Mathematik, Vol. 178, Issue. 1, p. 39.


    MIERNOWSKI, TOMASZ and NOGUEIRA, ARNALDO 2013. Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations. Ergodic Theory and Dynamical Systems, Vol. 33, Issue. 01, p. 221.


    Bruin, Henk and Jiménez López, Víctor 2010. On the Lebesgue Measure of Li-Yorke Pairs for Interval Maps. Communications in Mathematical Physics, Vol. 299, Issue. 2, p. 523.


    Barnes, Julia and Hawkins, Jane 2007. Families of ergodic and exact one-dimensional maps. Dynamical Systems, Vol. 22, Issue. 2, p. 203.


    Bruin, Henk and van Strien, Sebastian 2003. Expansion of derivatives in one-dimensional dynamics. Israel Journal of Mathematics, Vol. 137, Issue. 1, p. 223.


    ×
  • Ergodic Theory and Dynamical Systems, Volume 21, Issue 4
  • August 2001, pp. 1009-1034

Exactness and maximal automorphic factors of unimodal interval maps

  • HENK BRUIN (a1) and JANE HAWKINS (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385701001481
  • Published online: 01 August 2001
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.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax