Abstract: 

For surface self-homeomorphisms (e.g., pseudo-Anosov maps), the induced dynamics on isotopy classes of curves forms a well-established and fruitful theory. We will discuss analogous questions for postcritically finite (PCF) rational maps, such as the existence of spanning graphs of minimal entropy and the finite global attractor conjecture for the multivalued pullback operation on isotopy classes of graphs of prescribed complexity. We then prove the finiteness of such an attractor for maps with four postcritical points, excluding the usual Lattès counterexamples. The proof, which is joint work with L. Bartholdi and K. Pilgrim, relies on a detailed analysis of the non-uniform hyperbolicity of PCF correspondences on Riemann surfaces.

Zoom Meeting ID: 832 0847 3832 
Passcode: Ergodic