turkmath.org

This talk deals with exact reduction methods for dynamical systems, namely, the possibility of projecting the dynamics onto a smaller state space in which a self-contained dynamical description exists. The projection is also called lumping, aggregation, or reduction in various contexts, for example in Markov chains, and connects micro to macro in multi-level systems. As a first setting we consider systems whose evolution is described by bounded or unbounded linear operators on Banach spaces and obtain conditions for lumpability using semigroup theory. Time permitting, we will also present the problem from a dual space point of view in the language of sun dual spaces. We will give several examples for applications.