Definition 6 Consider a solution to Equations (16)–(17). Assume for some and that

Let . By Proposition 2, we get the conclusion that has smooth expansions in a neighborhood of . In particular, converges to a smooth function in , and the convergence is exponential in any -norm. By Proposition 1, . We call a nondegenerate false spike if .

Note that nondegenerate false spikes have punctured neighborhoods with normal expansions.

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