Topics in singularity theory : V.I. Arnold's 60th anniversary collection
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Topics in singularity theory : V.I. Arnold's 60th anniversary collection
（American Mathematical Society translations, ser. 2,
American Mathematical Society, c1997
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Includes references
This volume contains a selection of original papers prepared, on the occasion of Vladimir Igorevich Arnold's sixtieth anniversary, by his former students and other participants in his Moscow seminar
Description and Table of Contents
Description
'We were fortunate. We studied under Arnold. We moved in his orbit and had the opportunity to discuss with him everything under the sun. For every one of us this was a rare gift, a great good fortune in our lives' - from the Introduction. Leading mathematician and expert teacher, V. I. Arnold turned 60 in June of 1997. This volume contains a selection of original papers prepared for the occasion of this 60th anniversary by former students and other participants in Arnold's Moscow seminar. A weekly event since the mid-1960s, this seminar and its participants have been inspired by Arnold's creative ideas and universal approach to mathematics.The papers in this volume reflect Arnold's wide range of interests and his scientific contributions, including singularity theory, symplectic and contact geometry, mathematical physics, and dynamical systems. The spirit of this work is consistent with Arnold's view of mathematics, connecting different areas of mathematics and theoretical physics. The book is rich in applications and geometrical in nature.
Table of Contents
On the geometry of caustics by J. W. Bruce and V. M. Zakalyukin Lagrangian embeddings and Lagrangian cobordism by Yu. V. Chekanov Polynomial invariants of Legendrian links and plane fronts by S. Chmutov and V. Goryunov Solutions of the elliptic qKZB equations and Bethe ansatz I by G. Felder, V. Tarasov, and A. Varchenko Singular deformations of Lie algebras. Example: Deformations of the Lie algebra $L_1$ by A. Fialowski and D. Fuchs On imaginary plane curves and spin quotients of complex surfaces by complex conjugation by S. Finashin and E. Shustin Stationary phase integrals, quantum toda lattices, flag manifolds and the mirror conjecture by A. Givental On a problem of B. Teissier by S. M. Gusein-Zade Embedding theorems for local maps, slow-fast systems and bifurcation from Morse-Smale to Smale-Williams by Yu. Ilyashenko Topological invariants of fiber singularities by M. E. Kazaryan Informal complexification and Poisson structures on moduli spaces by B. A. Khesin Consistent partitions of polytopes and polynomial measures by A. Khovanskii On primitive elements in the bialgebra of chord diagrams by S. K. Lando Spaces of meromorphic functions on Riemann surfaces by S. M. Natanzon Hamiltonian loops and Arnold's principle by L. Polterovich Singularities in the presence of symmetries by I. Scherbak Discrete versions of the four-vertex theorem by V. D. Sedykh Excitation of elliptic normal modes of invariant tori in Hamiltonian systems by M. B. Sevryuk Ramified coverings of $S^2$ with one degenerate branching point and enumeration of edge-ordered graphs by B. Shapiro, M. Shapiro, and A. Vainshtein On zeros of the Schwarzian derivative by S. Tabachnikov Stratified Picard-Lefschetz theory with twisted coefficients by V. A. Vassiliev.
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