, Volume 105, Issue 1, pp 123-136

Invariant measures exist under a summability condition for unimodal maps

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Summary

For unimodal maps with negative Schwarzian derivative a sufficient condition for the existence of an invariant measure, absolutely continuous with respect to Lebesgue measure, is given. Namely the derivatives of the iterations of the map in the (unique) critical value must be so large that the sum of (some root of) the inverses is finite.

Oblatum 7-V-1990 & 19-XI-1990
Partially supported by the NWO grant.