Topics On Real And Complex Singularities

by Satoshi Koike, Toshizumi Fukui, Laurentiu Paunescu, Adam Harris, Alexander Isaev

Overview

A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings.This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians.

Product Details

ISBN-13:	9789814596039
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/17/2014
Pages:	212
Product dimensions:	6.00(w) x 9.10(h) x 0.80(d)

Table of Contents

On the CR Hamiltonian Flows and CR Yamabe Problem (T Akahori); An Example of the Reduction of a Single Ordinary Differential Equation to a System, and the Restricted Fuchsian Relation (K Ando); Fronts of Weighted Cones (T Fukui and M Hasegawa); Involutive Deformations of the Regular Part of a Normal Surface (A Harris and K Miyajima); Connected Components of Regular Fibers of Differentiable Maps (J T Hiratuka and O Saeki); The Reconstruction and Recognition Problems for Homogeneous Hypersurface Singularities (A V Isaev); Openings of Differentiable Map-Germs and Unfoldings (G Ishikawa); Non Concentration of Curvature near Singular Points of Two Variable Analytic Functions (S Koike, T-C Kuo and L Paunescu); Saito Free Divisors in Four Dimensional Affine Space and Reflection Groups of Rank Four (J Sekiguchi); Holonomic Systems of Differential Equations of Rank Two with Singularities along Saito Free Divisors of Simple Type (J Sekiguchi); Parametric Local Cohomology Classes and Tjurina Stratifications for µ-Constant Deformations of Quasi-Homogeneous Singularities (S Tajima).