turkmath.org

The goal in dynamics is to study the long-term behavior of orbits. Even for apparently simple systems the goal might be dicult and even out of reach. This is frequently the case when several variables are involved. Behavior might be dierent depending on directions, some directions might be contracting while others might be expanding without any uniformity. The questions become accessible in holomorphic dynamics because powerful methods are available. I will describe some recent progress in several variables holomorphic dynamics, centered on ergodic theory and equidistribution problems. Appropriate space of observables play a crucial r^ole.