Another Proof of Jakobson’s Theorem and Related Results

Summary

The author shows that any family C ²-close to f _a (x) = 1 − ax ² (2 − ε ≤ a ≤ 2) satisfies Jakobson’s theorem: For a positive measure set of a the transformation f _a has an absolutely continuous invariant measure. He also indicates some generalizations.

This article was originally published in journal form in Ergod. The. & Dynam. Sys. (1988), 8, 93–109. With kind permission from the publishers it is included in this volume. The author’s address at the time of writing of this article was: University of Washington, Department of Mathematics, GN-50, Seattle, Washington 98195 USA and Institute of Mathematics, University of Warsaw, Poland