Bifurcations and random matrix theory

The divergence of semiclassical amplitudes at periodic orbit bifurcations h as strong effects on long-range spectral statistics. We discuss the statist ical weight of such effects in parameter pace, using as an example the quan tised standard map a a function of the kicking strength. The parameter inte rval affected by saddle-node bifurcations is independent of (h) over bar an d determined by classical dynamics. In the distribution P(t) of the traces of the evolution operator the bifurcations contribute an algebraically deca ying part that exceeds the exponentially decaying RMT part for large traces . Specifically, for saddle-node bifurcations P(t) similar to t(-3) up to t similar to (h) over bar (-1/6).