Topological Conditions for the Existence of Invariant Measures for Unimodal Maps

摘要

We present a class of S-unimodal maps having an invariant measure which isabsolutely continuous with respect to Lebesgue measure. This measure can often be proved to be finite. We given an example of a map which has such a finite measure and for which the liminf 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 these same properties. (Copyright (c) 1992 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)