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.
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Oblatum 7-V-1990 & 19-XI-1990
Partially supported by the NWO grant.
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Nowicki, T., van Strien, S. Invariant measures exist under a summability condition for unimodal maps. Invent Math 105, 123–136 (1991). https://doi.org/10.1007/BF01232258
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DOI: https://doi.org/10.1007/BF01232258