Rare events in dynamical systems

The study of rare events in dynamical systems is currently one of the most active branches of research in ergodic theory. In part, this is due to their interesting applications in earth and ocean sciences. An example of a rare event in dynamical systems appears in the study of 'open' systems where orbits infrequently escape from the domain, typically by falling into a small "hole" in the phase space. The gaol of the project is to use spectral techniques (via the so called Perron-Frobenius operator) to approximate escape rates in open systems and to compute the Hausdorff dimension of survival sets.