EVENT DETAILS AND ABSTRACT

Title: Rational maps: Topology and Dynamics
Speaker: Dylan Thurston
Speaker Info: Indiana University - Bloomington
Brief Description:
Special Note:
Abstract:

We look at rational maps like $f(z) = 1 - 1/z^2$ from a topological point of view, as developed by William Thurston in 1982. This amounts to looking at rational maps as topological maps from the sphere to itself, up to suitable homotopy. Unlike in more traditional settings, different dynamical quantities grow at different rates. In fact, there are dynamical "degrees" $\overline{E}^p$ depending on a continuous parameter $p \in [1,\infty]$. The energy for $p=2$ controls whether a topological map is a rational map at all, and in general the energy gives information on the conformal dimension of the Julia set.