Date:	Mon, November 17, 2014
Time:	14:15
Place:	Research I Seminar Room

Abstract: Given a rational map f, there are two natural measure on the Riemann sphere: the measure of maximal entropy, and the Lebesgue measure. Zdunik's theorem says that these measures are singular unless f is a Lattes map. I will present a proof in the simpler case when f is postcritically finite. The focus will be on methods, such as the Ruelle operator, lifts of inverses to the orbifold cover. If time permits, I will give two other characterizations of Lattes maps, one in terms of the visual metric, on in terms of combinatorics (due to Q. Yin).