Asymptotics of ramified integrals

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
Savin A. 1, 2 , Sternin B. 1, 2
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
Short link
https://repository.rudn.ru/en/records/article/record/5896/