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Decay of geometry for unimodal maps: an elementary proof. (English) Zbl 1097.37032

Summary: We prove that a nonrenormalizable smooth unimodal interval map with critical order between 1 and 2 displays decay of geometry, by an elementary and purely “real” argument. This completes a “real” approach to Milnor’s attractor problem for smooth unimodal maps with critical order not greater than 2.

MSC:

37E05 Dynamical systems involving maps of the interval
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