Carl Dettmann (Bristol University)
Escape from systems with small holes.
<br><br>
Abstract: A dynamical system may be "opened" by allowing trajectories to
leak out through one or more holes, a subset of phase space. Given a
distribution of initial conditions, We can then pose questions about the
probability of surviving within the system, as a function of time, the 
size
and position of the hole(s). Open billiard dynamics can be related to a
number of physical experiments and applications involving escape of
particles from a cavity. In several geometries the leading coefficient of
the survival probability can be determined, including connections with the
Riemann Hypothesis and phenomena such as asymmetric transport. Recent and
detailed results for escape and diffusion in one-dimensional maps will 
also
be discussed.