Fields Institute Communications 1999; 555 pp; hardcover Volume: 24 ISBN10: 0821809458 ISBN13: 9780821809457 List Price: US$116 Member Price: US$92.80 Order Code: FIC/24
 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 overincluding 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 copublished 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 threewave 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 EnriquesEinsteinHitchin 4manifolds
 W. Ebeling and S. M. GuseinZade  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 GromovWitten 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 AndronovHopf and BogdanovTakens 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 apriori stable, three degreeoffreedom 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
