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Distortion results and invariant Cantor sets of unimodal maps

Published online by Cambridge University Press:  19 September 2008

Marco Martens
Marco Martens
Affiliation:
Institute for Mathematical Sciences, State University of New York at Stony Brook, Stony BrookUSA
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Abstract

A distortion theory is developed for S-unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of S-unimodal maps is classified according to a distortion property, called the Markov-property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 2 , June 1994 , pp. 331 - 349
Copyright
Copyright © Cambridge University Press 1994

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References

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