LEAFWISE COHOMOLOGICAL EXPRESSION OF DYNAMICAL ZETA FUNCTIONS ON FOLIATED DYNAMICAL SYSTEMS (Analytic Number Theory and Related Topics)

Abstract

A Riemmanian foliated dynamical system of 3-dimension (RFDS3)is a closed Riemannian 3-manifold with additional structures: foliation, dynamical system. In the context of arithmetic topology, it is a geometric/analytic analogue of an arithmetic scheme with a conjectural dynamical system suggested by C. Deninger. In this paper, we show leafwise cohomological expression of dynamical zeta function on a Riemannian foliated dynamical system.