Abstract:

The linear distortion of iterates plays a crucial role in smooth one-dimensional dynamics and is usually estimated using the Koebe Lemma. However, cross-ratio estimates are required. Classically, these were only assured for maps with negative Schwarzian derivative. Kozlovski proved that the Schwarzian condition is not necessary for $C3$ unimodal maps with non-flat critical point. We can now prove this for maps which are only $C2$ - where the Schwarzian is not even defined.