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.

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[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

  1. 1 2 Terras (2010) p. 28
  2. Terras (2010) p. 29
This article is issued from Wikipedia - version of the 6/1/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.