11 The Generic Set, General T3-Gowdy

There are general results concerning the asymptotic behavior in the direction of the singularity for T3-Gowdy spacetimes; there is, e.g., an open and dense subset ℰ of the circle such that there are smooth expansions on ℰ; see [12, Theorem 1.3, p. 1018] and [79Jump To The Next Citation Point, Proposition 1.9, p. 985]. However, the results of [546871] show that the asymptotic behavior of solutions is in general very complicated; there are, e.g., solutions with an infinite number of true spikes. On the other hand, much of the complicated behavior can be expected to be unstable, i.e., nongeneric. Thus, since the strong cosmic-censorship conjecture is only a statement concerning generic solutions, it is natural to try to find a set of solutions whose asymptotics are generic but less complicated than those of general solutions. The purpose of the present section is to define one generic set of initial data. Since the concepts nondegenerate true and false spikes play a central role, let us begin by defining them.

 11.1 Nondegenerate true spikes
 11.2 Nondegenerate false spikes
 11.3 The generic set, definition
 11.4 Verification of genericity, openness
 11.5 Verification of genericity, density

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