|Date:||Wed, May 3, 2017|
|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.