Ruelle zeta function
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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
Summarize
Perspective
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]
Examples
In the special case d = 1, φ = 1, we have[1]
which is the Artin–Mazur zeta function.
The Ihara zeta function is an example of a Ruelle zeta function.[2]
See also
References
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