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Vladimir Arnold Collected Works: Singularity Theory 19721979 1st ed. 2016 [Hardback]

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  • Formāts: Hardback, 509 pages, height x width: 244x170 mm, weight: 1030 g, 51 Illustrations, black and white; XIV, 509 p. 51 illus., 1 Hardback
  • Sērija : Vladimir I. Arnold - Collected Works 3
  • Izdošanas datums: 07-Oct-2016
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662496127
  • ISBN-13: 9783662496121
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Vladimir Arnold Collected Works: Singularity Theory 19721979 1st ed. 2016Palielināt
  • Formāts: Hardback, 509 pages, height x width: 244x170 mm, weight: 1030 g, 51 Illustrations, black and white; XIV, 509 p. 51 illus., 1 Hardback
  • Sērija : Vladimir I. Arnold - Collected Works 3
  • Izdošanas datums: 07-Oct-2016
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662496127
  • ISBN-13: 9783662496121
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783662496121.html
Keywords:
Volume III of the Collected Works of V.I. Arnold contains papers written in the years 1972 to 1979. The main theme emerging in Arnold's work of this period is the development of singularity theory of smooth functions and mappings.





The volume also contains papers by V.I. Arnold on catastrophe theory and on A.N. Kolmogorov's school, his prefaces to Russian editions of several books related to singularity theory, V. Arnold's lectures on bifurcations of discrete dynamical systems, as well as a review by V.I. Arnold and Ya.B. Zeldovich of V.V. Beletsky's book on celestial mechanics.



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 Modes and Quasimodes
Funct. Anal. Appl. 6(2), 94-101 (1972). Translation of Funkts. Anal. Prilozh. 6(2), 12-20 (1972)
1(8)
2 Integrals of Rapidly Oscillating Functions and Singularities of Projections of Lagrangian Manifolds
Funct. Anal. Appl. 6(3), 222-224 (1972). Translation of Funkts. Anal. Prilozh. 6(3), 61-62 (1972)
9(4)
3 Remarks on the Stationary Phase Method and Coxeter Numbers
Russ. Math. Surveys 28(5), 19-48 (1973). Translation of Usp. Mat. Nauk 28(5), 17-44 (1973)
13(30)
4 Normal Forms of Functions near Degenerate Critical Points, the Weyl Groups Ak, Dk, Ek, and Lagrangian Singularities
Published as "Normal Forms for Functions near Degenerate Critical Points, the Weyl Groups of Ak, Dk, Ek and Lagrangian Singularities" in: Funct. Anal. Appl. 6(4), 254-272 (1972). Translation of Funkts. Anal. Prilozh. 6(4), 3-25 (1972)
43(20)
5 Normal Forms of Functions in Neighbourhoods of Degenerate Critical Points
Russ. Math. Surveys 29(2), 10-50 (1974). Translation of Usp. Mat. Nauk 29(2), 11-49 (1974)
63(42)
6 Critical Points of Functions and Classification of Caustics
Translation of Usp. Mat. Nauk 29(3), 243-244 (1974)
105(4)
Boris Khesin
Andrey Khesin
7 Classification of Unimodal Critical Points of Functions
Funct. Anal. Appl. 7(3), 230-231 (1973). Translation of Funkts. Anal. Prilozh. 7(3), 75-76 (1973)
109(2)
8 Classification of Bimodal Critical Points of Functions
Funct. Anal. Appl. 9(1), 43-44 (1975). Translation of Funkts. Anal. Prilozh. 9(1), 49-50 (1975)
111(2)
9 Spectral Sequence for Reduction of Functions to Normal Form
Funct. Anal. Appl. 9(3), 251-253 (1975). Translation of Funkts. Anal. Prilozh. 9(3), 81-82 (1975)
113(4)
10 Spectral Sequences for Reducing Functions to Normal Forms
Selecta Math. Sovietica 1(1), 3-18 (1981). Translation of "Problems in Mechanics and Mathematical Physics". Moscow: Nauka, 7-20 (1976)
117(16)
11 Critical Points of Smooth Functions and Their Normal Forms
Russ. Math. Surveys 30(5), 1-75 (1975). Translation of Usp. Mat. Nauk 30(5), 3-65 (1975)
133(76)
12 Local Normal Forms of Functions
Invent. Math. 35(1), 87-109 (1976)
209(24)
13 Some Open Problems in Singularity Theory
Published as "Some Open Problems in the Theory of Singularities" in: Singularities. Part 1 (Arcata, CA, 1981), Amer. Math. Soc., Providence, R.I., 57-69 (Proc. Sympos. Pure Math. 40, Part 1) (1983). Translation of "Theory of Cubature Formulas and Applications of Functional Analysis to Problems in Mathematical Physics", Trudy Sem. S.L. Soboleva, No. 1, Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk, 5-15 (1976)
233(14)
14 On the Theory of Envelopes
Translation of Usp. Mat. Nauk 31(3), 248-249 (1976)
247(2)
Boris Khesin
Andrey Khesin
15 Wave Front Evolution and Equivariant Morse Lemma
Comm. Pure Appl. Math. 29(6), 557-582 (1976)
249(26)
16 A Correction to: Wave Front Evolution and Equivariant Morse Lemma
Comm. Pure Appl. Math. 30(6), 823 (1977)
275(2)
17 A Conjecture on the Signature of the Quadratic Form of a Quasihomogeneous Singularity
Appendix 2 to the paper by S.M. Husein-Zade "The Monodromy Groups of Isolated Singularities of Hypersurfaces". Russ. Math. Surveys 32(2), 63-64 (1977). Translation of Usp. Mat. Nauk 32(2), 60-61 (1977)
277(2)
18 On Contemporary Developments of I.G. Petrovskii's Works on Topology of Real Algebraic Varieties
Translation of Usp. Mat. Nauk 32(3), 215-216 (1977)
279(2)
Boris Khesin
Andrey Khesin
19 Topology of Real Algebraic Varieties (with O.A. Oleinik)
Published as "Topology of Real Algebraic Manifolds" in: Moscow Univ. Math. Bull. 34(6), 5-17 (1979). Translation of Vestnik Mosk. Univ. Ser. I Mat. Mekh. 6, 7-17 (1979)
281(14)
20 Bifurcations of Invariant Manifolds of Differential Equations and Normal Forms of Neighborhoods of Elliptic Curves
Published as "Bifurcations of Invariant Manifolds of Differential Equations and Normal Forms in Neighborhoods of Elliptic Curves" in: Funct. Anal. Appl. 10(4), 249-259 (1976). Translation of Funkts. Anal. Prilozh. 10(4), 1-12 (1976)
295(12)
21 Loss of Stability of Self-Oscillations Close to Resonances and Versal Deformations of Equivariant Vector Fields
Published as "Loss of Stability of Self-Oscillations Close to Resonance and Versal Deformations of Equivariant Vector Fields" in: Funct. Anal. Appl. 11(2), 85-92 (1977). Translation of Funkts. Anal. Prilozh. 11(2), 1-10 (1977)
307(8)
22 Some Problems in the Theory of Differential Equations
Translation of "Unsolved Problems of Mechanics and Applied Mathematics", Moscow: Moscow Univ. Press, 3-9 (1977)
315(8)
Boris Khesin
Andrey Khesin
23 Bifurcations of Discrete Dynamical Systems
A.P. Shapiro
Translation of Preprint, Far Eastern Scientific Center, USSR Acad. Sciences, Inst. of Automation and Control Processes, Vladivostok, 24 pp (1977)
323(22)
Boris Khesin
Andrey Khesin
24 Index of a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequality, and Mixed Hodge Structures (in Russian)
Usp. Mat. Nauk 33(2), 179 (1978)
345(2)
25 Index of a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequalities, and Mixed Hodge Structures
Published as "Index of a Singular Point of a Vector Field, the Petrovskii-Oleinik Inequality, and Mixed Hodge Structures" in: Funct. Anal. Appl. 12(1), 1-12 (1978). Translation of Funkts. Anal. Prilozh. 12(1), 1-14 (1978)
347(12)
26 Critical Points of Functions on a Manifold with Boundary, the Simple Lie Groups Bk, Ck, and F4, and Singularities of Evolutes
Russ. Math. Surveys 33(5), 99-116 (1978). Translation of Usp. Mat. Nauk 33(5), 91-105 (1978)
359(18)
27 Indices of Singular Points of 1-Forms on a Manifold with Boundary, Convolution of Invariants of Reflection Groups, and Singular Projections of Smooth Surfaces
Russ. Math. Surveys 34(2), 1-42 (1979). Translation of Usp. Mat. Nauk 34(2), 3-38 (1979)
377(42)
28 Stable Oscillations with Potential Energy Harmonic in Space and Periodic in Time
Published as "Steady Oscillations with Potential Energy Harmonic in Space and Periodic in Time" in: J. Appl. Math. Mech. 43(2), 385-389 (1979). Translation of Prikl. Mat. Mekh. 43(2), 360-363 (1979)
419(6)
29 The Loss of Stability of Self-Induced Oscillations near Resonances
Translation of Nonlinear Waves, A.V. Gaponov-Grekhov (Ed.), Moscow: Nauka, 116-131 (1979)
425(16)
Boris Khesin
Andrey Khesin
30 Catastrophe Theory
Translation of the popular scientific magazine "Priroda", No. 10, 54-63 (1979)
441(16)
Boris Khesin
Andrey Khesin
31 Superposition of Algebraic Functions (with G. Shimura)
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 45-46 (1976)
457(2)
32 The A-D-E Classifications
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 46 (1976)
459(2)
33 Real Algebraic Geometry (the 16th Hilbert Problem)
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 50-51 (1976)
461(2)
34 Study of Singularities
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 58-59 (1976)
463(2)
35 Dynamical Systems and Differential Equations
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 59-60 (1976)
465(2)
36 Fixed Points of Symplectic Diffeomorphisms
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 66 (1976)
467(2)
37 Partial Differential Equations
In: Mathematical Developments Arising from Hilbert Problems (1974) (Proc. Sympos. Pure Math. 28), Amer. Math. Soc., Providence, R.I., 67-68 (1976)
469(2)
38 The Beginning of a New Style in the Scientific Literature (a Review of V.V. Beletsky's Book "Essays on the Motion of Celestial Bodies", Moscow: Nauka Publishing House, 1972) (with Ya.B. Zeldovich)
Translation of the popular scientific magazine "Priroda", No. 10, 115-117 (1973)
471(8)
Boris Khesin
Andrey Khesin
38a A Science Book of a New Style (a Review of V.V. Beletsky's Book "Essays on the Motion of Celestial Bodies", Moscow: Nauka Publishing House, 1972)
Ya. B. Zeldovich
Translation of Usp. Fiz. Nauk 112(3), 541-542 (1974)
479(4)
Boris Khesin
Andrey Khesin
39 On the First All-Union Mathematical Student Olympiad
A.A. Kirillov
V.M. Tikhomirov
M.A. Shubin
Translation of Usp. Mat. Nauk 30(4), 281-288 (1975)
483(10)
Boris Khesin
Andrey Khesin
40 A Regional Mathematical School in Syktyvkar
A.M. Vershik
D.B. Fuks
Ya. M. Eliashberg
Usp. Mat. Nauk 31(4), 301 (1976)
493(2)
41 Kolmogorov's School
Translation of the newspaper "Trud", May 27, p. 2 (1978)
495(4)
Boris Khesin
Andrey Khesin
42 Preface to the Collection "Singularities of Differentiable Mappings" of Russian Translations of Papers in English and French
V.I. Arnold (Ed.). Moscow: Mir, 1968, 5--7
499(2)
Boris Khesin
Andrey Khesin
43 Preface to the Russian Translation of the Book "Introduction a l'etude topologique des singularites de Landau"
F. Pham
V.I. Arnold (Ed.). Moscow: Mir, 1970, 5--6
501(2)
Boris Khesin
Andrey Khesin
44 Preface to the Russian Translation of the Book "Singular Points of Complex Hypersurfaces"
J. Milnor
V.I. Arnold (Ed.). Moscow: Mir, 1971, 5--6
503(2)
Boris Khesin
Andrey Khesin
45 Preface to the Russian Translation of the Book "Differentiable Germs and Catastrophes"
Th. Brocker
L. Lander
V.I. Arnold (Ed.). Moscow: Mir, 1977, p. 5
505(2)
Boris Khesin
Andrey Khesin
46 Preface to the Russian Translation of the Book "Stable Mappings and Their Singularities"
M. Golubitsky
V. Guillemin
V.I. Arnold (Ed.). Moscow: Mir, 1977, p. 5
507(2)
Boris Khesin
Andrey Khesin
Acknowledgements 509
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.