  In many non-integrable open systems in physics and mathematics resonances
have been found to be surprisingly ordered along curved lines in the complex
plane. In this article we provide a unifying approach to these resonance chains
by generalizing dynamical zeta functions. By means of a detailed numerical
study we show that these generalized zeta functions explain the mechanism that
creates the chains of quantum resonance and classical Ruelle resonances for
3-disk systems as well as geometric resonances on Schottky surfaces. We also
present a direct system-intrinsic definition of the continuous lines on which
the resonances are strung together as a projection of an analytic variety.
Additionally, this approach shows that the existence of resonance chains is
directly related to a clustering of the classical length spectrum on multiples
of a base length. Finally, this link is used to construct new examples where
several different structures of resonance chains coexist.
