p-adic Julia sets and geometrically finite rational maps |
| Hongming Nie |
| Stony Brook University (USA) |
| Abstract: |
| A rational map defined over a finite extension \[K\] of the \[p\] -adic field \[\mathbb{Q}_p\] induces dynamical systems on the projective spaces over \[K\] and over \[\mathbb{C}_p\] , respectively, which gives two Julia sets (the non-equicontinunity regions in the projective spaces): the \[K\] -Julia set and the \[\mathbb{C}_p\] -Julia set. In this talk, I will show that the \[K\] -Julia set is a natural restriction of the \[\mathbb{C}_p\] -Julia set under some natural conditions. If time permits, I will talk about the dynamics on the \[K\] -Julia set for geometrically finite rational maps. This is a joint work with Fan, Liao and Wang. |