DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 857-866

Grzegorz Swiatek

Title: Induced Hyperbolicity for One-Dimensional Maps

We present a review of Yoccoz partitions and their relation with induced dynamics. A new way of interpreting the construction is shown, based on external Yoccoz partitions. These are governed by linear dynamics and hence much easier to handle. As an example of the usefulness of this method we prove the following result: For almost every parameter $c$ on the boundary of the Mandelbrot set, in the sense of the harmonic measure, the map $z^{2}+c$ satisfies the Collet-Eckmann condition.

1991 Mathematics Subject Classification: 30C10, 30D05

Keywords and Phrases: Yoccoz partition, Collet-Eckmann condition

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