GEODESIC FLOWS ON NEGATIVELY CURVED MANIFOLDS AND THE SEMI-CLASSICAL ZETA FUNCTION

摘要

In this article, we report some recent advances in the study of spectral properties of transfer operators for geodesic flows on negatively curved manifolds. We first review related studies, explaining important concepts and introduce basic definitions. We then discuss recent results on spectral properties of the (generator of) transfer operators and also related analytic properties of dynamical zeta functions.