Overview

It is very tempting but a little bit dangerous to compare the style of two great mathematicians or of their schools. I think that it would be better to compare papers from both schools dedicated to one area, geometry and to leave conclusions to a reader of this volume. The collaboration of these two schools is not new. One of the best mathematics journals Functional Analysis and its Applications had I.M. Gelfand as its chief editor and V.I. Arnold as vice-chief editor. Appearances in one issue of the journal presenting remarkable papers from seminars of Arnold and Gelfand always left a strong impact on all of mathematics. We hope that this volume will have a similar impact. Papers from Arnold's seminar are devoted to three important directions developed by his school: Symplectic Geometry (F. Lalonde and D. McDuff), Theory of Singularities and its applications (F. Aicardi, I. Bogaevski, M. Kazarian), Geometry of Curves and Manifolds (S. Anisov, V. Chekanov, L. Guieu, E. Mourre and V. Ovsienko, S. Gusein-Zade and S. Natanzon). A little bit outside of these areas is a very interesting paper by M. Karoubi Produit cyclique d'espaces et operations de Steenrod.

Full Product Details

Author:   V. Arnold ,  I.M. Gelfand ,  Mikhail Smirnov ,  Vladimir S. Retakh
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1997
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.674kg
ISBN:  

9781461286639

ISBN 10:   1461286638
Pages:   438
Publication Date:   26 September 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Discriminants and Local Invariants of Planar Fronts.- Crofton Densities, Symplectic Geometry and Hilbert’s Fourth Problem.- Projective Convex Curves.- Topological Classification of Real Trigonometric Polynomials and Cyclic Serpents Polyhedron.- Singularities of Short Linear Waves on the Plane.- New Generalizations of Poincaré’s Geometric Theorem.- Explicit Formulas for Arnold’s Generic Curve Invariants.- Nonlinear Integrable Equations and Nonlinear Fourier Transform.- Elliptic Solutions of the Yang-Baxter Equation and Modular Hypergeometric Functions.- Combinatorics of Hypergeometric Functions Associated with Positive Roots.- Local Invariants of Mappings of Surfaces into Three-Space.- Theorem on Six Vertices of a Plane Curve Via Sturm Theory.- The Arf—Invariant and the Arnold Invariants of Plane Curves.- Produit cyclique d’espaces et opérations de Steenrod.- Characteristic Classes of Singularity Theory.- Value of Generalized Hypergeometric Function at Unity.- Harish-Chandra Decomposition for Zonal Spherical Function of type An.- Positive Paths in the Linear Symplectic Group.- Invariants of Submanifolds in Euclidean Space.- On Combinatorics and Topology of Pairwise Intersections of Schubert Cells in SLn/B.

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