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| Date: | Wed, May 3, 2017 |
| Time: | 14:15 |
| Place: | Research I Seminar Room |
Abstract: The Fatou-Shishikura-inequality states that every rational map of degree d has at most 2d-2 periodic orbits that are attracting or indifferent. A weak version was proved by Fatou about 100 years ago, the sharp version is due to Shishikura in the 1980s. More recently, Adam Epstein found a novel proof that is conceptually very different and that also applies to transcendental functions, and that in some cases yields a somewhat stronger result. The proof is essentially self-contained; it uses quadratic differentials and their push-forward properties, and these will be introduced in the talk as well.