  Due to existence of periodic windows, chaotic systems undergo numerous
bifurcations as system parameters vary, rendering it hard to employ an analytic
continuation, which constitutes a major obstacle for its effective analysis or
computation. In this manuscript, however, based on cycle expansions we found
that spectral functions and thus dynamical averages are analytic, if symbolic
dynamics is preserved so that a perturbative approach is indeed possible. Even
if it changes, a subset of unstable periodic orbits (UPOs) can be selected to
preserve the analyticity of the spectral functions. Therefore, with the help of
cycle expansions, perturbation theory can be extended to chaotic regime, which
opens a new avenue for the analysis and computation in chaotic systems.
