In the previous chapter, we saw that the singularities of ramified integrals lie on Landau manifolds. So the question then arises about a more precise description of these singularities. The aim of this chapter is to answer this question. In more detail, we study ramified integrals near generic points of Landau manifolds. Namely, we show that the ramification of the homology class, over which we integrate, is described by Picard-Lefschetz formulas and that the asymptotics of the integral is given by Leray’s formulas. Slightly simplifying the situation, the main result can be formulated as follows: generically, near regular points of the Landau manifold, ramified integrals have singularities of one of the three types: square root singularity, logarithmic singularity, or pole. © Springer International Publishing AG 2017.

Authors

Collection of articles

Publisher

Birkhauser Verlag AG

Number of issue

9783319517438

Language

English

Pages

31-42

Status

Published

Year

2017

Organizations

^{1}RUDN University, Department of Applied Mathematics, Moscow, Russian Federation^{2}Leibniz Universität Hannover, Institut für Analysis, Hannover, Germany

Date of creation

19.10.2018

Date of change

19.10.2018