  We reason in support of the universality of quantum spectral fluctuations in
chaotic systems, starting from the pioneering work of Sieber and Richter who
expressed the spectral form factor in terms of pairs of periodic orbits with
self-crossings and avoided crossings. Dropping the restriction to uniformly
hyperbolic dynamics, we show that for general hyperbolic two-freedom systems
with time-reversal invariance the spectral form factor is faithful to
random-matrix theory, up to quadratic order in time. We relate the action
difference within the contributing pairs of orbits to properties of stable and
unstable manifolds. In studying the effects of conjugate points, we show that
almost self-retracing orbit loops do not contribute to the form factor. Our
findings are substantiated by numerical evidence for the concrete example of
two billiard systems.
