Dynamical systems occur as models in all the physical sciences. One dimensional dynamical systems have been studied to great depth but their use as models is limited. Higher dimensional systems have recently received great attention but they tend to be much more complicated. We propose to study complex dynamical systems in dimensions two and higher. The main emphasis is on the set where the dynamical behavior is orderly, called the Fatou set. In one complex dimension the Fatou set is completely understood but in higher dimensions many important problems are completely open. The reintegration grant will enable us to create an excellent research environment for complex dynamical systems in Amsterdam. Funds from the grant will be used to support the research of the applicant, set up a complex dynamics seminar at the University of Amsterdam, invite guests to Amsterdam and organise a workshop in several complex variables. The grant will also allow the applicant to spend one semester in the United States where he will solidify his connections with strong complex dynamics groups at SUNY Stony Brook and the University of Michigan.