Ruelle zeta function

In mathematics, the Ruelle zeta function is a zeta function associated with a dynamical system.

It is named after mathematical physicist David Ruelle.

Let f be a function defined on a manifold M, such that the set of fixed points Fix(f n) is finite for all n > 1.

Further let φ be a function on M with values in d × d complex matrices.

The zeta function of the first kind is[1] In the special case d = 1, φ = 1, we have[1] which is the Artin–Mazur zeta function.