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001 978-3-642-31031-7
003 DE-He213
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008 131211s2014 gw | s |||| 0|eng d
020 _a9783642310317
_9978-3-642-31031-7
024 7 _a10.1007/978-3-642-31031-7
_2doi
050 4 _aQC19.2-20.85
072 7 _aPBWH
_2bicssc
072 7 _aMAT003000
_2bisacsh
082 0 4 _a519
_223
100 1 _aArnold, Vladimir I.
_eauthor.
245 1 0 _aVladimir I. Arnold - Collected Works
_h[electronic resource] :
_bHydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972 /
_cby Vladimir I. Arnold ; edited by Alexander B. Givental, Boris A. Khesin, Alexander N. Varchenko, Victor A. Vassiliev, Oleg Ya. Viro.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2014.
300 _aXIII, 465 p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aVladimir I. Arnold - Collected Works ;
_v2
505 0 _a1 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 as functions 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 the universe -- 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.
520 _aVladimir 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. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aMathematical Applications in the Physical Sciences.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aMathematical Methods in Physics.
700 1 _aGivental, Alexander B.
_eeditor.
700 1 _aKhesin, Boris A.
_eeditor.
700 1 _aVarchenko, Alexander N.
_eeditor.
700 1 _aVassiliev, Victor A.
_eeditor.
700 1 _aViro, Oleg Ya.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642310300
830 0 _aVladimir I. Arnold - Collected Works ;
_v2
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-31031-7
912 _aZDB-2-SMA
999 _c93130
_d93130