Geodesic
Asymptotics of two-dimensional integrals depending singularity on a small parameter
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 5-11

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The asymptotics is constructed for integrals of form $\iint\limits_w \frac{dxdy}{\epsilon^2+\chi(x,y)}$ where $\omega$ is some vicinity of a critical point $(0,0)$ in which function $\chi(x,y)$ is equal to zero. It is considered the case in which function $\chi(x,y)$ addresses in a zero on two crossed curves and has a special appearance. 
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     author = {A. A. Ershov},
     title = {Asymptotics of two-dimensional integrals depending singularity on a small parameter},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {5--11},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a0/}
}
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A. A. Ershov. Asymptotics of two-dimensional integrals depending singularity on a small parameter. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 5-11. http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a0/