Titlebook: Singularities of Differentiable Maps, Volume 2; Monodromy and Asympt V.I. Arnold,S.M. Gusein-Zade,A.N. Varchenko Book 2012 Springer Science

CEDE

Discussion of resultsThe problems of optics, acoustics and quantum mechanics, the theory of partial differential equations, probability theory and number theory lead to the need to study oscillatory integrals with large values of the parameter.

Kindle

裂口

orthodox

The simplest properties of the integralsIn this chapter we shall prove the holomorphic dependence of the integral on the parameters; we shall explain the connection between branches of integrals and the monodromy group in homology; we shall prove that the integral can be expanded in a series in a neighbourhood of the given value of the parameter.

政府

Ganglion

牛馬之尿

The topology of the non-singular level set and the variation operator of a singularitytheorem that in a neighbourhood of the origin in the space .the level setf-l .for for ε≠0 is a non-singular analytic manifold and the level set . is a nonsingular manifold away from the origin. At the point . the level set has a singular point.

frivolous

單純

The intersection matrices of singularities of functions of two variables[147], [148]) and N. A’Campo ([7], [8]). It applies to all singularities oftwo variables. Using it allows us substantially to simplify many calculations connected with the quadratic form of a singularity (for example, the calculation of its signature).

LARK

The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectruilnor fibration ofa critical point. The function given by the integral can be expanded in a series ofpowers ofthe parameter and powers ofthe logarithm ofthe parameter ofthe family (Chapter 1O). Each coefficient ofthe series depends linearly both on the form and on the continuous family ofintegral homologies.