Real Analytic and Algebraic Singularities  book cover
1st Edition

Real Analytic and Algebraic Singularities

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ISBN 9780582328747
Published December 12, 1997 by Chapman and Hall/CRC
232 Pages

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Book Description

This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

Table of Contents

List of participants
Tzee-Char Kuo's contributions to real singularities
Blow-analytic equisingularities, properties, problems and progress
On blow-analytic equivalence of embedded curve singularities
On arc-analytic trivialization of singularities
Blow-analytic retraction onto the central fibre
An example of blow-analytic homeomorphism
The blow analytically constant stratum of real analytic singularities
Sufficiency of jets with respect to L-equivalence
A relative transversality theorem and its applications
Isomorphism of smooth map germs with isomorphic local algebra
Quelques proprietes de la distance geodesique
Relation between equivalence relations of maps and functions
Duality of the second fundamental form
Geometric study of quasilinear first order partial differnetial equations
Geometric approach to blow-up phenomena in non-linear problems
Multiplicity of complex analytic sets and bilipschitz maps
transcendence measures for subsets of local algebras
On topological invariance of weights for quasihomogeneous polynomials
Multiplicity as a C1 invariant

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Fukui\, Toshisumi; Izumiya\, Shuichi; Koike\, Satoshi; Fukuda\, Toshisumi