11.3 The generic set, definition

We are now in a position to give the definition of what, in the end, will turn out to be the generic set, [79Jump To The Next Citation Point, Definition 1.14, p. 988]:

Definition 7 Let š’¢l,m be the set of smooth solutions (Q, P) to Equations (16View Equation)–(17View Equation) on 1 ā„ × S with l nondegenerate true spikes šœƒ1,...,šœƒl and m nondegenerate false spikes šœƒ′1,...,šœƒ′m such that

lim Pτ(τ,šœƒ) = v∞ (šœƒ), τ→ ∞

for all ′ ′ šœƒ āˆ•∈ {šœƒ1,...,šœƒm} and 0 < v∞ (šœƒ) < 1 for all šœƒ āˆ•∈ {šœƒ1,...,šœƒl}. Let š’¢l,m,c be the set of (Q, P ) ∈ š’¢l,m such that

∫ (P τPšœƒ + e2PQ τQ šœƒ)dšœƒ = 0. (49 ) S1
Finally
∞ ∞ ∞ ∞ ā‹ƒ ā‹ƒ ā‹ƒ ā‹ƒ š’¢ = š’¢l,m, š’¢c = š’¢l,m,c. l=0m=0 l=0 m=0


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