Math Seminars.
Peter Balint (PSU)
Budapest University of Technology and Economics
Complexity of singularities and its role in the mixing properties multidimensional dispersing billiards
The talk focuses on multidimensional dispersing billiards (with
finite
horizon and no corner points) for which the complexity of singularities is
defined in rough terms as the maximal number of singularity components that may
meet in one point of the phase space. We prove, under sub-exponential growth of
this quantity, ergodicity and exponential decay of correlations for the
billiard
map. The talk is based on joint works with Pavel Bachurin and Imre Peter Toth.