Asymptotic expansions for some integrals of quotients with degenerated divisors

We study asymptotic expansion as $\nu \to 0$ for integrals over ${ $\mathbb{R}$ }^{2d}={(x,y)}$ofquotients$F(x,y) \big/ \big( (x\cdot y)^2+(\nu \Gamma(x,y))^2\big)^{-1}$,where$\Gamma$isstrictlypositiveand$F$ decays at infinity sufficiently fast. Integrals of this kind appear in description of the four–waves interactions.