The Arnoldfest

by Bierstone, Edward; Khesin, Boris; Khovanskii, Askold; Marsden, Jerrold E.

• ISBN13: 9780821809457
• ISBN10: 0821809458
• Format: Hardcover
• Copyright: 1999-11-01
• Publisher: Amer Mathematical Society

Summary

This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over--including several from "Arnold's school"--gave illuminating talks and lively poster sessions. The presentations focused on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program. The topics of the lectures are: (1) From Hilbert's Superposition Problem to Dynamical Systems (2) Symplectization, Complexification, and Mathematical Trinities (3) Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's "Recollections", concerning some of the history of KAM theory.

Table of Contents

Preface	xi
Program of the Conference	xiii
Photographs	xvi
From Hilbert's Superposition Problem to Dynamical Systems	1	(18)
V. I. Arnold
Recollections	19	(4)
Jurgen Moser
Symplectization, Complexification and Mathematical Trinities	23	(16)
V. I. Arnold
Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry	39	(16)
V. I. Arnold
Geometry and Control of Three-Wave Interactions	55	(26)
Mark S. Alber
Gregory G. Luther
Jerrold E. Marsden
Jonathan M. Robbins
Standard Basis Along a Samuel Stratum, and Implicit Differentiation	81	(34)
Edward Bierstone
Pierre D. Milman
A Global Weighted Version of Bezout's Theorem	115	(16)
James Damon
Real Enriques Surfaces Without Real Points and Enriques-Einstein-Hitchin 4-Manifolds	131	(10)
Alexander Degtyarve
Viatcheslav Kharlamov
On the Index of a Vector Field at an Isolated Singularity	141	(12)
W. Ebeling
S. M. Gusein-Zade
The Exponential Map on Dsμ	153	(12)
David G. Ebin
Gerard Misiolek
Zeldovich's Neutron Star and the Prediction of Magnetic Froth	165	(8)
Michael H. Freedman
Arnold Conjecture and Gromov-Witten Invariant for General Symplectic Manifolds	173	(18)
Kenji Fukaya
Kaour Ono
Multiplicity of a Zero of an Analytic Function on a Trajectory of a Vector Field	191	(10)
Andrei Gabrielov
Singularity Theory and Symplectic Topology	201	(8)
Alexander B. Givental
On Enumeration of Meromorphic Functions on the Line	209	(16)
V. V. Goryunov
S. K. Lando
Pseudoholomorphic Curves and Dynamics	225	(16)
H. Hofer
E. Zehnder
Bifurcation of Planar and Spatial Polycycles: Arnold's Program and Its Development	241	(32)
Yu. S. Ilyashenko
V. Yu. Kaloshin
Singularity Which Has No M-Smoothing	273	(38)
V. M. Kharlamov
S. Yu. Orevkov
E. I. Shustin
Symplectic Geometry on Moduli Spaces of Holomorphic Bundles over Complex Surfaces	311	(14)
Boris Khesin
Alexei Rosly
Newton Polyedra, a New Formula for Mixed Volume, Product of Roots of a System of Equations	325	(40)
A. Khovanskii
Interactions of Andronov-Hopf and Bogdanov-Takens Bifurcations	365	(20)
William F. Langord
Kaijun Zhan
Solutions of the qKZB Equation in Tensor Products of Finite Dimensinal Modules Over the Elliptic Quantum Group E&tau,ηsl2	385	(12)
E. Mukhin
A. Varchenko
Schrodinger Operators on Graphs and Sympletic Geometry	397	(18)
S. P. Novikov
On the Dominant Fourier Modes in the Series Associated with Separatix Splitting for an A-Priori Stable, Three Degree-of-Freedom Hamiltonian System	415	(36)
Michael Rudnev
Stephen Wiggins
Homology of i-Connected Graphs and Invariants of Knots, Plane Arrangemnets, etc.	451	(20)
V. A. Vassiliev
On Arnold's Variational Principles in Fluid Mechanics	471	(26)
V. A. Vladimirov
K. I. Ilin
On Functions and Curves Defined by Ordinary Differential Equations	497	(30)
Sergei Yakovenko
Global Finiteness Properties of Analytic Families and Algebra of Their Taylor Coefficients	527
Y. Yomdin