PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Boris Kalinin, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.

Title:Polynomials, eigenvalues, and Thurston's Theorem
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Sarah Koch, University of Michigan
Abstract:
In William Thurston's last paper, "Entropy in Dimension One," he completely characterizes which numbers arise as exp(entropy(f)), where f is a critically finite real polynomial map of a closed interval. Inspired by his work (and the spectacular fractal picture on page 1 of his manuscript), we consider a particular dynamical quantity associated to critically finite rational maps. Following earlier work of Thurston, a critically finite rational map induces a holomorphic endomorphism on a Teichmueller space, and this endomorphism has a unique fixed point. We study the spectrum of the derivative of this endomorphism and prove that there is a prominent spectral gap in the case of quadratic polynomials. We plot a picture for this data (analogous to Thurston's entropy picture), revealing some incredible fractal structure. This is joint work with X. Buff and A. Epstein.

Room Reservation Information

Room Number:MB114
Date:11 / 13 / 2013
Time:03:35pm - 04:35pm