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Exactness and maximal automorphic factors of unimodal interval maps

Published online by Cambridge University Press:  06 August 2001

HENK BRUIN  and
JANE HAWKINS
HENK BRUIN
Affiliation:
Mathematics Department 253-37, California Institute of Technology, Pasadena, CA 91125, USA
JANE HAWKINS
Affiliation:
Mathematics Department CB #3250, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA (e-mail: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 4 , August 2001 , pp. 1009 - 1034
Copyright
2001 Cambridge University Press

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