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Getting rid of the negative Schwarzian derivative condition. (English) Zbl 0988.37044
The author proves that for any \(C^3\) unimodal map of an interval with a non-flat critical point there exists an interval around the critical value such that the first entry map to this interval has negative Schwarzian derivative. Consequently, the assumption that such maps have negative Schwarzian derivative can be removed from the many theorems related to these maps. Thus, these unimodal maps are similar in many ways to univalent maps. The author also investigates cross ratios for these maps.

MSC:
37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
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