Vladimir I. Arnold - Collected Works

"Volume II focuses on hydrodynamics, bifurcation theory and algebraic geometry. ... Arnold was a very prolific writer. The publication of his collected works is a huge task and a great service to the mathematical community particularly since his papers appeared in various journals some of which are not easily accessible. ... I have no doubt that these volumes will be of great benefit to the current and future generations of researchers and graduate students." (Gerard Misiolek, zbMATH 1354.01038, 2017)

• 1 Variational principle for three-dimensional steady-state flows of an ideal fluid.- 2 On the Riemann curvature of diffeomorphism groups.- 3 Sur la topologie des écoulements stationnaires des fluides parfaits (in French).- 4 Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid.- 5 On the topology of three-dimensional steady flows of an ideal fluid.- 6 On an a priori estimate in the theory of hydrodynamical stability.- 7 On the differential geometry of infinite-dimensional Lie groups and its application to the hydrodynamics of perfect fluids.- 8 On a variational principle for the steady flows of perfect fluids and its application to problems of non-linear stability.- 9 Characteristic class entering in quantization conditions.- 10 A note on Weierstrass auxiliary theorem.- 11 A letter to the editors (in Russian).- 12 The stability problem and ergodic properties for classical dynamical systems.- 13 Remark on the branching of hyperelliptic integrals asfunctions of the parameters.- 14 Singularities of smooth mappings.- 15 Braids of algebraic functions and the cohomology of swallowtails.- 16 Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid.- 17 Remarks on singularities of finite codimension in complex dynamical systems.- 18 One-dimensional cohomologies of the Lie algebras of non-divergence vector fields, and rotation numbers of dynamic systems.- 19 The cohomology ring of the colored braid group.- 20 Trivial problems.- 21 Cohomology classes of algebraic functions invariant under Tschirnhausen transformations.- 22 Local Problems of Analysis.- 23 Algebraic unsolvability of the problem of stability and the problem of the topological classification of the singular points of analytic systems of differential equations (in Russian).- 24 On some topological invariants of algebraic functions.- 25 Topological invariants of algebraic functions II.- 26 Algebraic unsolvability of the problem of Ljapunov stability and the problem of the topological classification of singular points of an analytic system of differential equations.- 27 On matrices depending on parameters.- 28 Distribution of ovals of the real plane of algebraic curves of involutions of four-dimensional smooth manifolds and the arithmetic of integer valued quadratic forms.- 29 Versal families and bifurcations of differential equations (in Russian).- 30 Notes on the three-dimensional flow pattern of a perfect fluid in the presence of a small perturbation of the initial velocity field.- 31 Lectures on bifurcations in versal families.- 32 The topology of real algebraic curves (in Russian).- 33 The asymptotic Hopf invariant and its applications.- 34 Magnetic field in a moving conducting fluid.- 35 A magnetic field in a stationary flow with stretching in a Riemannian space.- 36 The large-scale structure of the universe I. General properties. One- and two-dimensional models.- 37 Elements of the large-scale structure of theuniverse.- 38 Some remarks on the antidynamo theorem.- 39 Steady-state magnetic field in a periodic flow.- 40 Evolution of a magnetic field under the action of transfer and diffusion.- 41 The growth of a magnetic field in a three-dimensional steady incompressible fluid.- 42 Evolution of a magnetic field under the action of drift and diffusion (in Russian).- 43 Exponential scattering of trajectories and its hydrodynamical applications.- 44 Kolmogorov's hydrodynamic attractors.- 45 Topological methods in hydrodynamics.- 46 Problemes mathématiques de l'hydrodynamique et de la magnétohydrodynamique (in English).- 47 Translator's Preface to J. Milnor's book "Morse Theory".- 48 Henri Poincaré: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics - Preface. From the editorial board. Comments.- 49 Comments on the paper "On a geometric theorem" by Henri Poincaré.