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Friday, March 01, 2019
3:00 PM - 5:00 PM
Linde Hall 187

Geometry and Topology Seminar

Classification of hyperbolic component with bounded escape
Yusheng Luo, Department of Mathematics, Harvard University ,

A hyperbolic component is said to have bounded escape if there is a sequence of rational maps which is degenerating as conjugacy classes, but for any period $p$, the multipliers of periodic points of period $p$ remain bounded. A hyperbolic component is said to have nested Julia set if the Julia set is a Cantor set of nested continuum.

In this talk, we will study the barycentric extensions of rational maps on hyperbolic $3$ space and its geometric limit as branched coverings on a $\R$-tree.

We will use them to show that a hyperbolic component has bounded escape if and only if it has nested Julia set.

We remark that either phenomenon cannot happen for a finitely generated Kleinian group.

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].