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Topological conditions for the existence of invariant measures for unimodal maps

Published online by Cambridge University Press:  19 September 2008

H. Bruin
H. Bruin
Affiliation:
Delft University of Technology, Department of Pure Mathematics, PO Box 5031, 2600 GA Delft, The Netherlands
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Abstract

We present a class of S-unimodal maps having an invariant measure which is absolutely continuous with respect to Lebesgue measure. This measure can often be proved to be finite. We give an example of a map which has such a finite measure and for which the lim inf of the derivatives of the iterates of the map in the critical value is finite. It will be shown that all topologically conjugate non-flat S-unimodal maps have the same properties.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 14 , Issue 3 , September 1994 , pp. 433 - 451
Copyright
Copyright © Cambridge University Press 1994

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