Geodesic
Asymptotic behaviors of integrals, and Hodge structures
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 130-166
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The survey is devoted to the asymptotics of integrals of the method of descent and to the Hodge structures of critical points of phases of integrals. The problem of how asymptotics change under deformation of phases is discussed. 
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     author = {A. N. Varchenko},
     title = {Asymptotic behaviors of integrals, and {Hodge} structures},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {130--166},
     year = {1983},
     volume = {22},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1983_22_a3/}
}
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A. N. Varchenko. Asymptotic behaviors of integrals, and Hodge structures. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 130-166. http://geodesic.mathdoc.fr/item/INTD_1983_22_a3/