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Hardcover ISBN:  9780821808078 
Product Code:  TRANS2/180 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470433918 
Product Code:  TRANS2/180.E 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
Hardcover ISBN:  9780821808078 
eBook ISBN:  9781470433918 
Product Code:  TRANS2/180.B 
List Price:  $340.00 $257.50 
MAA Member Price:  $306.00 $231.75 
AMS Member Price:  $272.00 $206.00 

Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 180; 1997; 255 ppMSC: Primary 57; 58; Secondary 00
“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 mid1960s, 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.
ReadershipGraduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

Table of Contents

Chapters

J. W. Bruce and V. M. Zakalyukin — On the geometry of caustics

Yu. V. Chekanov — Lagrangian embeddings and Lagrangian cobordism

S. Chmutov and V. Goryunov — Polynomial invariants of Legendrian links and plane fronts

G. Felder, V. Tarasov and A. Varchenko — Solutions of the elliptic qKZB equations and Bethe ansatz I

Alice Fialowski and Dmitry Fuchs — Singular deformations of Lie algebras. Example: Deformations of the Lie algebra $L_1$

Sergeĭ Finashin and Eugeniĭ Shustin — On imaginary plane curves and spin quotients of complex surfaces by complex conjugation

Alexander Givental — Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture

S. M. GuseinZade — On a problem of B. Teissier

Yu. Ilyashenko — Embedding theorems for local maps, slowfast systems and bifurcation from MorseSmale to SmaleWilliams

Maxim È. Kazaryan — Topological invariants of fiber singularities

Boris A. Khesin — Informal complexification and Poisson structures on moduli spaces

A. Khovanskiĭ — Consistent partitions of polytopes and polynomial measures

S. K. Lando — On primitive elements in the bialgebra of chord diagrams

S. M. Natanzon — Spaces of meromorphic functions on Riemann surfaces

Leonid Polterovich — Hamiltonian loops and Arnold’s principle

Inna Scherbak — Singularities in the presence of symmetries

V. D. Sedykh — Discrete versions of the fourvertex theorem

M. B. Sevryuk — Excitation of elliptic normal modes of invariant tori in Hamiltonian systems

B. Shapiro, M. Shapiro and A. Vainshtein — Ramified coverings of $S^2$ with one degenerate branching point and enumeration of edgeordered graphs

Serge Tabachnikov — On zeros of the Schwarzian derivative

Victor A. Vassiliev — Stratified PicardLefschetz theory with twisted coefficients


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“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 mid1960s, 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.
Graduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

Chapters

J. W. Bruce and V. M. Zakalyukin — On the geometry of caustics

Yu. V. Chekanov — Lagrangian embeddings and Lagrangian cobordism

S. Chmutov and V. Goryunov — Polynomial invariants of Legendrian links and plane fronts

G. Felder, V. Tarasov and A. Varchenko — Solutions of the elliptic qKZB equations and Bethe ansatz I

Alice Fialowski and Dmitry Fuchs — Singular deformations of Lie algebras. Example: Deformations of the Lie algebra $L_1$

Sergeĭ Finashin and Eugeniĭ Shustin — On imaginary plane curves and spin quotients of complex surfaces by complex conjugation

Alexander Givental — Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture

S. M. GuseinZade — On a problem of B. Teissier

Yu. Ilyashenko — Embedding theorems for local maps, slowfast systems and bifurcation from MorseSmale to SmaleWilliams

Maxim È. Kazaryan — Topological invariants of fiber singularities

Boris A. Khesin — Informal complexification and Poisson structures on moduli spaces

A. Khovanskiĭ — Consistent partitions of polytopes and polynomial measures

S. K. Lando — On primitive elements in the bialgebra of chord diagrams

S. M. Natanzon — Spaces of meromorphic functions on Riemann surfaces

Leonid Polterovich — Hamiltonian loops and Arnold’s principle

Inna Scherbak — Singularities in the presence of symmetries

V. D. Sedykh — Discrete versions of the fourvertex theorem

M. B. Sevryuk — Excitation of elliptic normal modes of invariant tori in Hamiltonian systems

B. Shapiro, M. Shapiro and A. Vainshtein — Ramified coverings of $S^2$ with one degenerate branching point and enumeration of edgeordered graphs

Serge Tabachnikov — On zeros of the Schwarzian derivative

Victor A. Vassiliev — Stratified PicardLefschetz theory with twisted coefficients