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|
|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
|Date:||11 / 13 / 2013|
|Time:||03:35pm - 04:35pm|