In mathematics, the Ruelle zeta function is a zeta function associated with a dynamical system. It is named after mathematical physicist David Ruelle.
Formal definition 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 isTerras (2010) p. 28
Examples In the special case d = 1, φ = 1, we have
which is the Artin–Mazur zeta function.
The Ihara zeta function is an example of a Ruelle zeta function.Terras (2010) p. 29
See also List of zeta functions
References