, Volume 133, Issue 1, pp 69-96

Collet, Eckmann and Hölder

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We prove that Collet-Eckmann condition for rational functions, which requires exponential expansion only along the critical orbits, yields the Hölder regularity of Fatou components. This implies geometric regularity of Julia sets with non-hyperbolic and critically-recurrent dynamics. In particular, polynomial Collet-Eckmann Julia sets are locally connected if connected, and their Hausdorff dimension is strictly less than 2. The same is true for rational Collet-Eckmann Julia sets with at least one non-empty fully invariant Fatou component.

Oblatum 22-III-1996 & 15-VII-1997