Gregory Hemenway
The Ohio State University
Title
Invariant Families of Measures in Non-stationary Dynamics
Abstract
Historically, the Ruelle-Perron-Frobenius (RPF) theorem provided a fundamental framework for understanding the long-term behavior of dynamical systems and their associated equilibrium states. In the 1990s and early 2000s, mathematicians like Kifer and Simmons-Urbanski studied equilibrium states for random systems, where the dynamics are chosen probabilitisically from a class of maps at each iteration. In particular, they used fiberwise transfer operators to construct families of measures that are invariant under the dynamics almost everywhere.
We will discuss new results on the construction of families of measures for some non-stationary systems (a generalization of random systems). Specifically, we will demonstrate how the Hilbert metric, a powerful tool for analyzing convex cones in Banach spaces, can be employed to establish a non-stationary RPF theorem.
