Lemma 4.3 . [03FK]

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Lemma 4.3.

As $\beta\to\infty,\beta^{\vee}\to 0$ , the linear map

d\psi\circ J_{Z_{a}}\circ(d\psi)^{-1}-J_{W_{a}}:T_{x}{W_{a}}\to T_{x}{W_{a}}

is of order $C_{\lambda-c,\nu}(\beta)\cdot O(\frac{1}{\beta^{\vee}}e^{-\beta})$ .