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Dynamical Systems VIII: Singularity Theory II. Applications
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Catalogue Information
Field name
Details
Dewey Class
514.2
Title
Dynamical Systems VIII ([EBook]) : Singularity Theory II. Applications / edited by V. I. Arnol’d.
Added Personal Name
Arnold, Vladimir Igorevic , 1937-2010. editor.
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 1993.
Physical Details
VI, 238 pages : online resource.
Series
Encyclopaedia
of
mathematical sciences
0938-0396 ; ; 39
ISBN
9783662067987
Summary Note
In the first volume
of
this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods
of
the theory
of
singularities
of
smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent
of
the first one: all
of
the concepts
of
singularity theory that we use are introduced in the course
of
the presentation, and references to EMS 6 are confined to the citation
of
technical results. Although our main goal is the presentation
of
analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some
of
these results. 2 3 In the consideration
of
mappings from C into C in§ 3. 6
of
Chapter 1, we define the bifurcation diagram
of
such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams
of
simple singularities, give the definition
of
the Mond invariant N in the spirit
of
"hunting for invariants", and we draw the reader's attention to a method
of
constructing the image
of
a mapping from the corresponding function on a manifold with boundary. In§ 4. 6
of
the same chapter we introduce the concept
of
a versal deformation
of
a function with a nonisolated singularity in the dass
of
functions whose critical sets are arbitrary complete intersections
of
fixed dimension.:
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-662-06798-7
Links to Related Works
Subject References:
Algebraic Geometry
.
Algebraic Topology
.
Analysis (Mathematics)
.
Complex manifolds
.
Manifolds and Cell Complexes (incl. Diff.Topology)
.
Manifolds (Mathematics)
.
Mathematical analysis
.
Theoretical, Mathematical and Computational Physics
.
Authors:
Arnold, Vladimir Igorevic, 1937-2010.
.
editor
.
Corporate Authors:
SpringerLink (Online service)
.
Series:
Encyclopaedia
of
mathematical sciences
.
Classification:
514.2
.
.
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