A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation

Michel Lapidus and Machiel van Frankenhuysen

Assuming some regularity of the dynamical zeta function, we establish an explicit formula with an error term for the prime orbit counting function of a suspended flow. We define the subclass of self-similar flows, for which we give an extensive analysis of the error term in the corresponding prime orbit theorem.