ABSTRACT:

I present an example of a three-dimensional dispersing billiard with finite horizon, where the usual ``sub-exponential complexity condition'' on the structure of the singularity set fails to hold. This condition is typicaly used in proving strong statistical properties through the Perron-Frobenius spectrum. I try to argue why the Perron-Frobenius operator of such a system cannot be handled on Banach spaces based on Hšlder-type norms.