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Symmetric S-unimodal mappings and positive Liapunov exponents

Published online by Cambridge University Press:  19 September 2008

Tomasz Nowicki
Tomasz Nowicki
Affiliation:
IZMiS, SGGW-AR, Nowoursynowska 166, Warsaw, Poland
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Abstract

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Symmetric S-unimodal functions with positive Liapunov exponent of the critical value have an invariant measure absolutely continuous with respect to Lebesgue measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 4 , December 1985 , pp. 611 - 616
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Collet, P.. Ergodic properties of some unimodal mappings of the interval. Preprint, Institut Mittag-Leffler, Report no. 11, 1984.CrossRefGoogle Scholar
[2]Collet, P. & Eckmann, J.-P.. Interated Maps on the Interval as Dynamical Systems. Birkhauser: Basel, Boston, Stuttgart, 1980.Google Scholar
[3]Collet, P. & Eckmann, J.-P.. Positive Liapunov exponents and absolute continuity for maps of the interval. Ergod. Th. & Dynam. Sys. 3 (1983), 13–46.CrossRefGoogle Scholar