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Positive Liapunov exponents and absolute continuity for maps of the interval

Published online by Cambridge University Press:  19 September 2008

P. Collet  and
J.-P. Eckmann
P. Collet
Affiliation:
Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, France
J.-P. Eckmann
Affiliation:
Département de Physique Théorique, Universite de Genève, 1211 Genève 4, Switzerland
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Abstract

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We give a sufficient condition for a unimodal map of the interval to have an invariant measure absolutely continuous with respect to the Lebesgue measure. Apart from some weak regularity assumptions, the condition requires positivity of the forward and backward Liapunov exponent of the critical point.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 1 , March 1983 , pp. 13 - 46
Copyright
Copyright © Cambridge University Press 1983

References

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