Extension of the dynamics of unstable systems

The work of the Brussels-Austin groups over the last six years has demonstr ated that for unstable systems, classical or quantum, there exist spectral decompositions of the evolution in terms of resonances and resonance states which appear as eigenvalues and eigenprojections of the evolution operator . These new spectral decompositions are nontrivial only for unstable system s and define an extension of the evolution to suitable dual pairs. Duality here is the states/observables duality and the spectral decompositions exte nd the algebraic approach to dynamical systems to an intrinsically probabil istic and irreversible formulation. The extended formulation allows for pro babilistic prediction and control beyond the traditional local techniques.