AIM Workshop: Dynamics of multiple maps

This workshop, sponsored by AIM and the NSF, will be devoted to studying arithmetic dynamics of multiple maps. In classical arithmetic dynamics, we consider the iteration of a single endomorphism of a variety defined over a field of arithmetic interest — typically a number field or the function field of a curve. An exciting new direction in arithmetic dynamics that holds particular promise for striking new results is what we call "dynamics of multiple maps": dynamical behavior arising from the interaction of two or more endomorphisms on the same space. This includes iteratively applying rational functions on P1 chosen at random from a family according to some probability distribution; a correspondence from a variety X to itself; and forming words from a non-commuting family of involutions on a K3-surface.