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El. knyga: Vladimir I. Arnold - Collected Works: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972

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  • Formatas: PDF+DRM
  • Serija: Vladimir I. Arnold - Collected Works 2
  • Išleidimo metai: 11-Dec-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642310317
Kitos knygos pagal šią temą:
Vladimir I. Arnold - Collected Works: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972Didesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Vladimir I. Arnold - Collected Works 2
  • Išleidimo metai: 11-Dec-2013
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Kalba: eng
  • ISBN-13: 9783642310317
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Here is the second volume of the collected works of one of the great mathematical scientists of our time, renowned both for the breadth and depth of his work. This publication focuses on his research in hydrodynamics, bifurcation theory and algebraic geometry.

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. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.

Recenzijos

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 Misioek, zbMATH 1354.01038, 2017)

1 A variational principle for three-dimensional steady flows of an ideal fluid
Published as "Variational Principle for three-dimensional steady-state flows of an ideal fluid" in J. Appl. Math. Mech. 29:5, 1002-1008,
1965. Translation ofPrikl. Mat. Mekh. 29:5, 846-851, 1965
1(8)
2 On the Riemann curvature of diffeomorphism groups
Translation of C.R. Acad. Sc. Paris 260, 5668-5671, 1965
9(6)
Denis Auroux
3 Sur la topologie des ecoulements starionnaires des fluides parfaits (French)
C. R. Acad. Sc. Paris 261, 17-20, 1965
15(4)
4 Conditions for non-linear stability of stationary plane curvilinear flows of an ideal fluid
Sov. Math. Dokl. 162, No. 5, 773-777,
1965. Translation of Dokl. Akad. Nauk SSSR, 162:5, 975-978, 1965
19(6)
5 On the topology of three-dimensional steady flows of an ideal fluid
J. Appl. Math. Mech. 30:1, 223-226
1966. Translation of Prikl. Mat. Mekh. 30:1, 183-185, 1966
25(4)
6 On an a priori estimate in the theory of hydrodynamical stability
Am. Math. Soc. Transl. (2) 79, 267-269,
1969. Translation of lzv. Vyssh. Uchebn. Zaved. Mat. 5:54, 3-5, 1966
29(4)
7 On the differential geometry of infinite-dimensional Lie groups and its applications to the hydrodynamics of perfect fluids
Translation of Annales de L'Institut Fourier, Vol. 16, No. 1, 319-361, 1966
33(38)
Alain Chenciner
8 On a variational principle for the steady flows of perfect fluids and its applications to problems of non-linear stability
Translation of Journal de Mecanique, Vol. 5, No. 1, 29-43, 1966
71(14)
Alain Chenciner
9 On a characteristic class arising in quantization conditions
Published as "Characteristic class entering in quantization conditions" in Funct. Anal. Appl. 1, 1-13,
1967. Translation of Funkts. Anal. Prilozh. 1:1, 1-14, 1967
85(14)
10 A note on the Weierstrass preparation theorem
Published as "A note on Weierstrass' auxiliary theorem" in Funct. Anal. Appl. I, 173-179,
1967. Translation of Funkts. Anal. Prilozh. 1:3, 1-8, 1967
99(8)
11 The stability problem and ergodic properties for classical dynamical systems
Am. Math. Soc. Transl. (2) 70, 5-11,
1969. Translation of Proc. lnternat. Congr. Math., Moscow 1966, 387-392, 1968
107(8)
12 A remark on the ramification of hyperelliptic integrals as functions of parameters
Published as "Remark on the branching of hyperelliptic integrals as functions of the parameters" in Funct. Anal. Appl. 2, 187-189,
1968. Translation of Funkts. Anal. Prilozh. 2:3, 1-3, 1968
115(4)
Victor Vassiliev
13 Singularities of smooth mappings
Russ. Math. Surv. 23, 1-43,
1968. Translation of Usp. Mat. Nauk 23:1, 3-44, 1968
119(44)
14 Remarks on singularities of finite codimension in complex dynamical systems
Funct. Anal. Appl. 3, 1-5,
1969. Translation of Funkts. Anal. Prilozh. 3:1, 1-6, 1969
163(8)
Victor Vassiliev
15 Braids of algebraic functions and the cohomology of swallowtails
Translation of Usp. Mat. Nauk 23:4, 247-248, 1968
171(4)
Gerald Gould
16 Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid
Translation of Usp. Mat. Nauk 24:3, 225-226, 1969
175(4)
Gerald Gould
17 On the one-dimensional cohomology of the Lie algebra of divergence-free vector fields and rotation numbers of dynamical systems
Published as "One-dimensional cohomologies of the Lie algebras of nondivergent vector fields and rotation numbers of dynamic systems" in Funct. Anal. Appl. 3, 319-321,
1969. Translation of Funkts. Anal. Prilozh. 3:4, 77-78, 1969
179(4)
Victor Vassiliev
18 The cohomology ring of the colored braid group
Math. Notes 5, 138-140,
1969. Translation of Mat. Zametki 5:2, 227-231, 1969
183(4)
Victor Vassiliev
19 On cohomology classes of algebraic functions invariant under Tschirnhausen transformations
Funct. Anal. Appl. 4, 74-75,
1970. Translation of Funkts. Anal. Prilozh. 4:1, 84-85, 1970
187(4)
Victor Vassiliev
20 Trivial problems
Translation of Proc. 5th Int. Conf. on Nonlinear Oscillations, Kiev
1969. Vol. 1, 630-631, Ukrain. Acad. Sciences, Kiev 1970
191(2)
Gerald Gould
21 Local problems of analysis
Moscow Univ. Math. Bull. 25 (1970), 77-80,
1970. Translation of Vestn. Mosk Univ. Ser. I, Mat. Mekh. 25:2, 52-56, 1970
193(4)
22 Algebraic unsolvability of the problem of stability and the problem of topological classification of singular points of analytic systems of differential equations (Russian)
Usp. Mat. Nauk 25:2, 265-266, 1970
197(2)
23 On some topological invariants of algebraic functions
Transact. Math. Moscow Soc. 21, 30-52,
1970. Translation of Tr. Mosk. Mat. Obsc., 27-46, 1970
199(24)
24 Topological invariants of algebraic functions II
Funct. Anal. Appl. 4, 91-98,
1970. Translation of Funkts. Anal. Prilozh. 4:2, 1-9, 1970
223(8)
25 Algebraic unsolvability of the problem of Lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations
Funct. Anal. Appl. 4, 173-180,
1970. Translation of Funkts. Anal. Prilozh. 4:3; 1-9, 1970
231(8)
26 On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms
Published as "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" in Funct. Anal. Appl. 5, 169-176,
1971. Translation of Funkts. Anal. Prilozh. 5:3, 1-9, 1971
239(12)
Oleg Viro
27 The topology of real algebraic curves (works of I.G. Petrovsky and their development)
Translation of Usp. Mat. Nauk 28:5, 260-262, 1973
251(4)
Oleg Viro
28 On matrices depending on parameters
Russ. Math. Surv. 22, 29-43,
1971. Translation of Usp. Mat. Nauk 26:2, 101-114, 1971
255(16)
29 Lectures on bifurcations in versal families
Russ. Math. Surv. 27, 54-123,
1972. Translation of Usp. Mat. Nauk 27:5, 119-184, 1972
271(70)
30 Versal families and bifurcations of differential equations (Russian)
Izd. Inst. Akad. Nauk Ukrain. SSR, Kiev, 42-49, 1972
341(8)
31 Remarks on the behaviour of a flow of a three-dimensional ideal fluid in the presence of a small perturbation of the initial vector field
Published as "Notes on the three-dimensional flow pattern of a perfect fluid in the presence of a small perturbation of the initial velocity field" in J. Appl. Math. Mech. 36:2, 236-242,
1972. Translation of Prikl. Mat. Mekh. 36:2, 255-262, 1972
349(8)
32 The asymptotic Hopf invariant and its applications
Selecta Math. Sov. 5:4, 327-345,
1986. Translation of Proc. All-Union School in Diff. Eq. with Infinite Number of Variables and in Dyn. Syst. with Infinite Number of Degrees of Freedom, Dilhan 1973, 229-256, 1974
357(20)
33 A magnetic field in a moving conducting fluid (with Ya.B. Zeldovich, A.A. Ruzmaikin, and D.D. Sokolov)
Translation of Usp. Mat. Nauk 36:5, 220-221, 1981
377(2)
Gerald Gould
34 A magnetic field in a stationary flow with stretching in a Riemannian manifold (with Ya.B. Zeldovich, A.A. Ruzmaikin, and D.D. Sokolov)
Published as "A magnetic field in a stationary flow with stretching in Riemannian space" in Sov. Phys. JETP 54:6, 1083-1086,
1982. Translation of Zh. Eksp. Teor. Fiz. 81:6, 2052-2056, 1981
379(4)
35 Stationary magnetic field in a periodic flow (with Ya.B. Zeldovich, A.A. Ruzmaikin, and D.D. Sokolov)
Published as "Steady-state magnetic field in a periodic flow" in Sov. Phys. Dok. 27:10, 814-816, 1982 Translation of Dokl. Akad. Nauk SSSR, 266:6, 1357-1361, 1982
383(4)
36 Some remarks on the antidynamo theorem
Moscow Univ. Math. Bull. 37, 57-66,
1982. Translation of Vestn. Mosk Univ. Ser. I, Mat. Mekh. 6, 50-57, 1982
387(10)
37 Evolution of a magnetic field under the action of transfer and diffusion
Translation of Usp. Mat. Nauk 38:2, 226-227, 1983
397(2)
Gerald Gould
38 The growth of a magnetic field in a three-dimensional steady incompressible flow (with E.I.Korkina)
Moscow Univ. Math. Bull, Ser. I, Math. Mech. 3, 50-54,
1983. Translation of Vestn. Mosk. Univ. Mat. 38:3, 43-46, 1983
399(6)
39 On evolution of a magnetic field under the action of drift and diffusion (Russian)
Some Problems in Modern Analysis, 8-21, MGU, Moscow 1984
405(14)
40 Exponential scattering of trajectories and its hydrodynamical applications
Translation of N.E. Kochin and the Development of Mechanics, 185-193, Nauka, Moscow 1984
419(10)
Gerald Gould
41 Kolmogorov's hydrodynamic attractors
Proc. Royal Soc. London A 434:1890, 19-22, 1991
429(4)
42 Topological methods in hydrodynamics (with B.A. Khesin)
Annu. Rev. Fluid Mech. 24, 145-166, 1992
433(22)
43 Translator's preface to J. Milnor's book "Morse Theory"
MIR, Moscow 1965
455(2)
Gerald Gould
44 Henri Poincare: Selected Works in Three Volumes. Vol. I New Methods of Celestial Mechanics -- Preface. From the editorial board Comments
Nauka, Moscow 1971, 747-752
457(6)
Gerald Gould
45 Comments on the paper "On a geometric theorem"
Henri Poincare
H. Poincare: Selected Works in Three Volumes. Vol. II. Klassiki Nauki, Nauka, Moscow 1972, 987-989
463(2)
Gerald Gould
Acknowledgements 465
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