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The Arnoldfest: Proceedings of a Conference in Honour of V. I. Arnold for his Sixtieth Birthday
Edited by: Edward Bierstone, Boris Khesin, and Askold Khovanskii, University of Toronto, ON, Canada, and Jerrold E. Marsden, California Institute of Technology, Pasadena, CA
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
1999; 555 pp; hardcover
Volume: 24
ISBN-10: 0-8218-0945-8
ISBN-13: 978-0-8218-0945-7
List Price: US$116
Member Price: US$92.80
Order Code: FIC/24
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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).

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

Table of Contents

  • V. I. Arnold -- From Hilbert's superposition problem to dynamical systems
  • J. Moser -- Recollections
  • V. I. Arnold -- Symplectization, complexification and mathematical trinities
  • V. I. Arnold -- Topological problems in wave propagation theory and topological economy principle in algebraic geometry
  • M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins -- Geometry and control of three-wave interactions
  • E. Bierstone and P. D. Milman -- Standard basis along a Samuel stratum, and implicit differentiation
  • J. Damon -- A global weighted version of Bezout's theorem
  • A. Degtyarev and V. Kharlamov -- Real Enriques surfaces without real points and Enriques-Einstein-Hitchin 4-manifolds
  • W. Ebeling and S. M. Gusein-Zade -- On the index of a vector field at an isolated singularity
  • D. G. Ebin and G. Misiołek -- The exponential map on \(\mathcal{D}^s_\mu\)
  • M. H. Freedman -- Zeldovich's neutron star and the prediction of magnetic froth
  • K. Fukaya and K. Ono -- Arnold conjecture and Gromov-Witten invariant for general symplectic manifolds
  • A. Gabrielov -- Multiplicity of a zero of an analytic function on a trajectory of a vector field
  • A. B. Givental -- Singularity theory and symplectic topology
  • V. V. Goryunov and S. K. Lando -- On enumeration of meromorphic functions on the line
  • H. Hofer and E. Zehnder -- Pseudoholomorphic curves and dynamics
  • Yu. S. Ilyashenko and V. Yu. Kaloshin -- Bifurcation of planar and spatial polycycles: Arnold's program and its development
  • V. M. Kharlamov, S. Yu. Orevkov, and E. I. Shustin -- Singularity which has no \(M\)-smoothing
  • B. Khesin and A. Rosly -- Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
  • A. Khovanskii -- Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations
  • W. F. Langford and K. Zhan -- Interactions of Andronov-Hopf and Bogdanov-Takens bifurcations
  • E. Mukhin and A. Varchenko -- Solutions of the qKZB equation in tensor products of finite dimensional modules over the elliptic quantum group \(E_{\tau,\eta}sl_2\)
  • S. P. Novikov -- Schrodinger operators on graphs and symplectic geometry
  • M. Rudnev and S. Wiggins -- On the dominant Fourier modes in the series associated with separatrix splitting for an a-priori stable, three degree-of-freedom Hamiltonian system
  • V. A. Vassiliev -- Homology of \(i\)-connected graphs and invariants of knots, plane arrangements, etc.
  • V. A. Vladimirov and K. I. Ilin -- On Arnold's variational principles in fluid mechanics
  • S. Yakovenko -- On functions and curves defined by ordinary differential equations
  • Y. Yomdin -- Global finiteness properties of analytic families and algebra of their Taylor coefficients
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