September 11, 2019
2:30 PM - 3:30 PM
Math Tower P-131
|Yusheng Luo, Stony Brook University|
R-trees for degenerating rational dynamics via Barycentric extensions and Berkovich spaces
We will study the barycentric extensions of rational maps to hyperbolic 3-space. By rescaling the metric, this allows us to construct limiting dynamics on R-trees. This construction is equivalent to the Berkovich construction using the complexified Robinson's field. We will study the dynamics in details and prove the ``difficult direction'' of ``bounded escape = nested Julia sets.'' Many other applications and open questions will be discussed.