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A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity

Published online by Cambridge University Press:  19 September 2008

Tomasz Nowicki
Tomasz Nowicki
Affiliation:
Warsaw Agricultural University, Department of Applied Mathematics, 02-766 Warsaw 166 Nowoursynowska, Poland
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Abstract

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A positive Liapunov exponent for the critical value of an S-unimodal mapping implies a positive Liapunov exponent of the backward orbit of the critical point, uniform hyperbolic structure on the set of periodic points and an exponential diminution of the length of the intervals of monotonicity. This is the proof of the Collet-Eckmann conjecture from 1981 in the general case.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 425 - 435
Copyright
Copyright © Cambridge University Press 1988

References

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