**Fields Institute Communications**

Volume: 24;
1999;
555 pp;
Hardcover

MSC: Primary 01; 14; 34; 57; 58; 76; 70;

Print ISBN: 978-0-8218-0945-7

Product Code: FIC/24

List Price: $122.00

Individual Member Price: $97.60

**Electronic ISBN: 978-1-4704-3048-1
Product Code: FIC/24.E**

List Price: $122.00

Individual Member Price: $97.60

# The Arnoldfest: Proceedings of a Conference in Honour of V. I. Arnold for his Sixtieth Birthday

Share this page *Edited by *
*Edward Bierstone; Boris Khesin; Askold Khovanskii; Jerrold E. Marsden*

A co-publication of the AMS and Fields Institute

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 focussed 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:

- From Hilbert's Superposition Problem to Dynamical Systems
- Symplectization, Complexification, and Mathematical Trinities
- 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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## The Arnoldfest: Proceedings of a Conference in Honour of V. I. Arnold for his Sixtieth Birthday

- Cover Cover11
- Title page v6
- Contents vii8
- Preface xi12
- Program xiii14
- Photos xvi17
- From Hilbert’s superposition problem to dynamical systems 120
- Recollections 1938
- Symplectization, complexification and mathematical trinities 2342
- Topological problems in wave propagation theory and topological economy principle in algebraic geometry 3958
- Geometry and control of three-wave interactions 5574
- Standard basis along a Samuel stratum, and implicit differentiation 81100
- A global weighted version of Bezout’s theorem 115134
- Real Enriques surfaces without real points and Enriques-Einstein-Hitchin 4-manifolds 131150
- On the index of a vector field at an isolated singularity 141160
- The exponential map on 𝒟^{𝓈}_{𝜇} 153172
- Zeldovich’s neutron star and the prediction of magnetic froth 165184
- Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds 173192
- Multiplicity of a zero of an analytic function on a trajectory of a vector field 191210
- Singularity theory and symplectic topology 201220
- On enumeration of meromorphic functions on the line 209228
- Pseudoholomorphic curves and dynamics 225244
- Bifurcation of planar and spatial polycycles: Arnold’s program and its development 241260
- Singularity which has no 𝑀-smoothing 273292
- Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces 311330
- Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations 325344
- Interactions of Andronov-Hopf and Bogdanov-Takens bifurcations 365384
- Solutions of the qKZB equation in tensor products of finite dimensional modules over the elliptic quantum group 𝐸_{𝜏,𝜂}𝑠𝑙₂ 385404
- Schrodinger operators on graphs and symplectic geometry 397416
- On the dominant Fourier modes in the series associated with separatrix splitting for an a-priori stable, three degree-of-freedom Hamiltonian system 415434
- Homology of 𝑖-connected graphs and invariants of knots, plane arrangements, etc. 451470
- On Arnold’s variational principles in fluid mechanics 471490
- On functions and curves defined by ordinary differential equations 497516
- Global finiteness properties of analytic families and algebra of their Taylor coefficients 527546
- Back Cover Back Cover1575

#### Readership

Graduate students and research mathematicians interested in singularity theory, the theory of curves, symmetry groups, dynamical systems, and mechanics; physicists and engineers interested in astronomy, mechanics, and bifurcation theory.

#### Reviews

The articles appearing in this volume illustrate diversity in mathematics stemming from a rather limited number of fundamental problems originally in Arnold's research … communicates esteem and warm affection for Arnold by his colleagues and former students.

-- CMS Notes

Provides an excellent record of the mathematical content of the conference, as well as an introduction to the mind of a great mathematician … these articles provide a wonderful autobiographical retrospective together with a wealth of mathematical ideas. They are a joy to read.

-- SIAM Review