VLADIMIR I. ARNOLD—Collected Works

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors.

• 1 Bernoulli–Euler updown numbers associated with function singularities, their combinatorics and arithmetics.- 2 Congruences for Euler, Bernoulli and Springer numbers of Coxeter groups.- 3 The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups.- 4 Springer numbers and Morsification spaces.- 5 Polyintegrable flows.- 6 Bounds for Milnor numbers of intersections in holomorphic dynamical systems.- 7 Some remarks on symplectic monodromy of Milnor fibrations.- 8 Topological properties of Legendre projections in contact geometry of wave fronts [On topological properties of Legendre projections in contact geometry of wave fronts].- 9 Sur les propriétés topologiques des projections lagrangiennes en géométrie symplectique des caustiques [On topological properties of Lagrangian projections in symplectic geometry of caustics].- 10 Plane curves, their invariants, perestroikas and classifications (with an appendix by F. Aicardi).- 11 Invariants and perestroikas of plane fronts.- 12 The Vassiliev theory of discriminants and knots.- 13 The geometry of spherical curves and the algebra of quaternions.- 14 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect.- 15 Problems on singularities and dynamical systems.- 16 Sur quelques problèmes de la théorie des systèmes dynamiques [On some problems in the theory of dynamical systems].- 17 Mathematical problems in classical physics.- 18 Problèmes résolubles et problèmes irrésolubles analytiques et géométriques [Solvable and unsolvable analytic and geometric problems].- 19 Projective topology.- 20 Questions à V.I. Arnold (an interview with M. Audin and P. Iglésias) [Questions to V.I. Arnold].- 21 En todo matemático hay un ángel y un demonio (an interview with Marimar Jiménez) [In every mathematician, there is an angel and a devil].- 22 Will Russian mathematics survive?.- 23 Will mathematics survive? Report on the Zurich Congress.- 24 Why study mathematics? What mathematicians think about it.- 25 Preface to the Russian translation of the book by M.F. Atiyah “The Geometry and Physics of Knots”.- 26 A comment on one of A.D. Sakharov’s “Amateur Problems”.- 27 Comments on two of A.D. Sakharov’s “Amateur Problems”.- Acknowledgements.