Dynamics Seminar

Event Information The large deviation principle in one-dimensional dynamics
15:10 on Wednesday November 23, 2016
16:00 on Wednesday November 23, 2016
BA6180, Bahen Center, 40 St. George St.
Juan Rivera-Letelier

University of Rochester

For uniformly hyperbolic diffeomorphisms, the large deviation principle was established in the late 1980s by Takahashi, Orey and Pelikan, Kifer, and Young. We show that the (level-2) large deviation principle for empirical means holds for every logistic map, in spite of the fact that the critical point is a serious obstruction to uniform hyperbolicity. In particular, the large deviation principle holds for the logistic maps without a physical measure found by Hofbauer and Keller, and leads to a somewhat paradoxical conclusion: averaged statistics hold, even for some systems without average asymptotics. This is a joint work with Yong Moo Chung and Hiroki Takahasi.