Speaker: Dr.Yi Yang(Peking University)
Title: Core decomposition for Julia sets
Time: Fri, Nov.15 2019,PM:14:30-15:30
Location: Room 4141, Building No.4, Wushan Campus
Abstract:
This work is mainly concerned with the topology of planar compacta motivated by applications to complex dynamics. Let \mathfrak{M}^{PC}(K) be the collection of all monotone decompositions of a planar compactum K with Peano compacta as their hyperspaces, we show that it has a unique member \mathcal{D}_K^{PC} finer than every other element. The decomposition \mathcal{D}_K^{PC} is called the core decomposition of K with Peano hyperspace. Then, for a planar compactum K and a rational function f, the core decomposition of the preimage of K under f is given by pulling back the core decomposition of K.