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A Riemmanian foliated dynamical system of 3-dimension $(\mathrm{RFDS}^{3})$is a closed Riemannian 3-manifold with additional structures: foliation,dynamical system. In the context of arithmetic topology, it is ageometric/analytic analogue of an arithmetic scheme with a conjecturaldynamical system suggested by C. Deninger. In this paper, we show leafwisecohomological expression of dynamical zeta function on a Riemannian foliateddynamical system.

Leafwise cohomological expression of dynamical zeta functions on foliated dynamical systems