Let f be a function defined on a
manifoldM, such that the set of
fixed points Fix(fn) 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]
Lapidus, Michel L.; van Frankenhuijsen, Machiel (2006). Fractal geometry, complex dimensions and zeta functions. Geometry and spectra of fractal strings. Springer Monographs in Mathematics. New York, NY:
Springer-Verlag.
ISBN0-387-33285-5.
Zbl1119.28005.