Dynamical systems are mathematical models describing the temporal evolution of real-world
processes which obey definite deterministic rules. Various such processes turn out to be chaotic,
which implies that even a complete description does not enable us to make detailed predictions
about their long-term behavior. For many important events it is then impossible to determine when
exactly they will occur. Still, in many cases the mathematical theory of dynamical systems allows us
to provide reliable predictions regarding statistical features like their overall frequency.
In some situations certain rare events are of great importance, in particular if they correspond to
extreme phenomena like natural disasters. The present project is devoted to the question when and
how, in certain types of chaotic systems, the statistical laws governing the occurrence of relevant
rare events can be predicted with certainty.