High velocity spikes in Gowdy spacetimes

We study the behavior of spiky features in Gowdy spacetimes. Spikes with a velocity initially high are, generally, driven to a low velocity. Let n be any integer greater than or equal to 1. If the initial velocity of an upward pointing spike is between 4n-3 and 4n-1 the spike persists with a final velocity between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the spiky feature eventually disappears. For downward pointing spikes the analogous rule is that spikes with an initial velocity between 4n-4 and 4n-2 persist with a final velocity between 0 and 1, while spikes with an initial velocity between 4n-2 and 4n eventually disappear.