11.5 Verification of genericity, density

Finally, [83Jump To The Next Citation Point, Theorem 2, p. 1190] yields the conclusion that š’¢ is dense:

Theorem 3 š’¢ and š’¢c are dense in š’®p and š’®p,c, respectively, with respect to the C ∞-topology on initial data.

Here š’®p and š’®p,c are defined in [83Jump To The Next Citation Point, Definition 1, p. 1188]:

Definition 8 Let š’®p denote the set of smooth solutions to Equations (16View Equation)–(17View Equation) on ā„ × S1, and let š’® p,c denote the subset of š’® p obeying

∫ 2P 1(P τPšœƒ + e Q τQ šœƒ)dšœƒ = 0. (50 ) S


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