Titlebook: Stable Mappings and Their Singularities; Martin Golubitsky,Victor Guillemin Textbook 1973 Springer-Verlag New York Inc. 1973 Immersion.Map

最小

Textbook 1973well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginn

套索

The Malgrange Preparation Theorem,ablish the existence of normal forms for singularities of certain stable mappings. In order to make the theorem palatable, we first state and prove the corresponding but less complicated result for analytic functions of several . variables.

辩论的终结

Preliminaries on Manifolds,Let . denote the real numbers and .. denote .-dimensional Euclidean space. Points of .. will be denoted by .-tuples of real numbers (..,..., ..) and .. will always be topologized in the standard way.

通便

Crayon

Various Equivalent Notions of Stability,In this section we have three objectives: to show that.We won’t be able to achieve our last objective just yet; but, at least, we shall be able to give a sufficient condition for the existence of a neighborhood of infinitesimally stable mappings around a given infinitesimally stable mapping.

和平主义

Graduate Texts in Mathematicshttp://image.papertrans.cn/s/image/875463.jpg

mydriatic

https://doi.org/10.1007/978-1-4615-7904-5Immersion; Mappings; Submersion; Umbilical point; manifold

飞镖

Connotation

Stable Mappings and Their Singularities978-1-4615-7904-5Series ISSN 0072-5285 Series E-ISSN 2197-5612

语言学

Textbook 1973arities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for