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 is
formula_1
Examples.
In the special case "d" = 1, "φ" = 1, we have
formula_2
which is the Artin–Mazur zeta function.
The Ihara zeta function is an example of a Ruelle zeta function.
References.
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