Rigorous estimates of invariant measures for expanding scalar maps

Dr. Brian Hunt

Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park

I will describe a method for obtaining a rigorous numerical estimate of the absolutely continuous invariant measure for a dynamical system from a class of one-dimensional expanding maps. An interesting application is to obtain a bound on a Lyapunov exponent of a polynomial map in the plane, which establishes that the map has "intermingled" basins of attraction. I will also discuss an algorithm for computing (approximate) trajectories of chaotic maps which can be proved, for the same class of maps as above, to be distributed according to the absolutely continuous invariant measure.