Vladimir I. Arnold - Collected Works: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972 Softcover reprint of the original 1st ed. 2014 [Minkštas viršelis]

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.