Various aspects of integrable Hamiltonian systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 36 (1981) no. 5 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{RM_1981_36_5_a30,
     author = {J. K. Moser},
     title = {Various aspects of integrable {Hamiltonian} systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     year = {1981},
     volume = {36},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/RM_1981_36_5_a30/}
}
TY  - JOUR
AU  - J. K. Moser
TI  - Various aspects of integrable Hamiltonian systems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 1981
VL  - 36
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/RM_1981_36_5_a30/
LA  - ru
ID  - RM_1981_36_5_a30
ER  - 
%0 Journal Article
%A J. K. Moser
%T Various aspects of integrable Hamiltonian systems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 1981
%V 36
%N 5
%U http://geodesic.mathdoc.fr/item/RM_1981_36_5_a30/
%G ru
%F RM_1981_36_5_a30
J. K. Moser. Various aspects of integrable Hamiltonian systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 36 (1981) no. 5. http://geodesic.mathdoc.fr/item/RM_1981_36_5_a30/

[1] V. I. Arnold, A. Avez, Problèmes Ergodiquies de la Mecanique Classique, Gauthier-Villars, Paris, 1967 | MR

[2] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[3] C. L. Siegel, J. K. Moser, Lectures on Celestial Mechanics, Springer, 1971 | MR | Zbl

[4] J. Moser, Stable and random motions in dynamical systems, Ann. Math. Studies, 77, 1973 | MR | Zbl

[5] M. Toda, “Wave propagation in anharmonic lattices”, J. Phys. Soc. Japan, 23 (1967), 501–506 | DOI

[6] M. Henon, Phys. Rev., 9 (1974), 1921–1923 | MR | Zbl

[7] H. Flaschka, “The Toda lattice, I”, Phys. Rev., 9 (1974), 1924–1925 ; Резюме докладов на заседаниях, посвященных 80-летию И. Г. Петровского, УМН, 36:4 (1981); см. [49] | MR | Zbl

[8] J. Moser, “Finitely many mass points on the line under the influence of an exponential potential — an integrable system”, Lecture Notes in Physics, 28, Springer, 1975, 467–497 | MR

[9] J. Moser, “Three integrable Hamiltonian systems connected with isospectral deformation”, Adv. Math., 16 (1975), 197–220 | DOI | MR | Zbl

[10] H. Airault, H. P. McKean, J. Moser, “Rational and elliptic Solution of the Korteweg-de Vries equation and a related many body problem”, Comm. Pure Appl. Math., 30 (1977), 95–148 | DOI | MR | Zbl

[11] M. Adler, J. Moser, “On a class of polynomials connected with the Korteweg-de Vries equation”, Comm. Math. Phys., 1978, 1–30 | DOI | MR | Zbl

[12] F. Calogero, Motion of poles and zeroes of special solutions of nonlinear and linear differential equations and related “solvable” many-body problems, preprint, Univ. di Poma, 1977 | MR

[13] D. V. Choodnovsky, G. V. Ghoodnovsky, “Pole expansions of nonlinear partial differential equations”, IL. Nuovo Cimento, 40 B (1977), 2 | MR

[14] M. A. Olshanetsky, A. M. Perelomov, “Completely integrable Hamiltonian systems connected with semisimple Lie algebras”, Invent. Math., 37 (1976), 93–109 | DOI | MR

[15] F. Calogero, “Exactly solvable one-dimentional many-body problems”, Lettres al Nuovo Cimento, 13:11 (1975), 411–416 | DOI | MR

[16] J. Marsden, A. Weinstein, “Reduction of symplectic manyfolds with symmetries”, Reports on Math. Physics, 5 (1974), 121–130 | DOI | MR | Zbl

[17] J. Marsden, Applications to Global Analysis in Mathematical Physics, Publish or Perish, Inc., 1974 | MR

[18] J. M. Souriau, Structure des systems dynamiques, Dynod, Paris, 1970 | MR

[19] A. A. Kirillov, Elementy teorii predstavlenii, Nauka, M., 1978 | MR | Zbl

[20] M. Adler, “On a trace functional for pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation”, Invent. Math., 50:3 (1979), 219–248 | DOI | MR | Zbl

[21] D. Kazhdan, B. Kostant, S. Sternberg, “Hamiltonian group actions and dynamical systems of Calogero type”, Comm. Pure Appl. Math., 31:4 (1978), 481–507 | DOI | MR | Zbl

[22] M. Adler, Completely integrable systems and symplectic actions, MRC Report 1830, Univ. Wisconsin, 1978 | Zbl

[23] F. Calogero, “Solutions of the one-dimensional $n$-body problems with quadratic and/or inversely quadratic pair potentials”, J. Math. Phys., 12 (1971), 419–436 | DOI | MR

[24] L. Bianchi, Vorlesungen über Differential geometrie, 2 deutsche Auflage, Teubner, 1910 | Zbl

[25] K. Yakobi, Lektsii po dinamike, ONTI, M.–L., 1936

[26] H. Schütt, Stabilität von periodischen Geodätischen auf $n$-dimensionalen Ellipsoiden, Dissertation, Bonn, 1972

[27] A. Thimm, Integrabilität bien geodätischen Fluss, Diplomarbeit, Bonn, 1976

[28] K. Weierstrass, Math. Werke, I, Mayer Muller, Berlin, 1894, p. 257–266 | Zbl

[29] D. Gilbert, S. Kon Fossen, Naglyadnaya geometriya.- M., Fizmatgiz, M.–L., 1951

[30] C. Neumann, “De problemate quodam mechanico, quod ad priman integralium ultraellipticorum classem revocatur”, J. reine Angew. Math., 56 (1859), 46–63 | Zbl

[31] K. Uhlenbeck, Minimal 2-spheres and tori in $S^k$, informal preprint, 1975 | Zbl

[32] R. Devaney, “Transversal homoclinic orbits in an integrable system”, Amer. J. Math., 1978, 631–642 | DOI | MR | Zbl

[33] E. Rosochatius, Über Bewegungen eines Punktes, Dissertation at Univ. Göttingen, Druck von Gebr. Unger, Berlin, 1877

[34] P. Stäckel, Über die Integration der Hamilton-Jacobischen Differential-gleichung mittelst Separation der Variablen, Habilitationsschrift, Halle, 1891 | Zbl

[35] B. A. Dubrovin, V. B. Matveev, S. P. Novikov, “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (1976), 55–136 | MR | Zbl

[36] V. A. Marchenko, I. V. Ostrovskii, “Kharakteristika spektra operatora Khilla”, Matem. sb., 97 (139) (1975), 493–554

[37] H. Hochstadt, “On the determination of Hill's equation from its spectrum”, Arch. Rat. Mech. Anal., 19 (1965), 353–362 | DOI | MR | Zbl

[38] H. P. McKean, P. van Moerbeke, “The spectrum of Hill's equation”, Invent. Math., 30 (1975), 217–274 | DOI | MR | Zbl

[39] H. P. McKean, E. Trubowitz, “Hill's operator and hypereliiptic function theory in the presence of infinitely many branch points”, Comm. Pure Appl. Math., 29 (1976), 14–226 | MR

[40] E. Trubowitz, “The inverse problem for periodic potentials”, Comm. Pure Appl. Math., 30 (1977), 321–337 | DOI | MR | Zbl

[41] N. Levinson, “The inverse Sturm-Liouville problem”, Mat. Tidsskr. B., 1949, 25–30 | MR

[42] S. V. Manakov, “Polnaya integriruemost i stokhastizatsiya v diskretnykh dinamicheskikh sistemakh”, ZhETF, 40 (1974), 269–274 | MR

[43] M. A. Olshanetsky, A. M. Perelomov, “Explicit solutions of classical generalized Toda models”, Invent. Math., 54 (1979), 261–269 | DOI | MR | Zbl

[44] B. Kostant, “The solution to a generalized Toda lattice and representation theory”, Adv. in Math., 34:3 (1980), 195–338 | DOI | MR

[45] M. A. Olshanetskii, A. M. Perelomov, “Tsepochka Toda kak redutsirovannaya sistema”, TMF, 45:1 (1980), 3–18 | MR

[46] D. R. Lebedev, Yu. I. Manin, “Gamiltonov operator Gelfanda-Dikogo i koprisoedinennoe predstavlenie gruppy Volterra”, Funkts. analiz, 13:4 (1980), 40–46 | MR

[47] A. M. Perelomov, “The simple relation between certain dynamical systems”, Comm. Math. Phys., 63 (1978), 9–11 | DOI | MR | Zbl

[48] M. A. Olshanetsky, A. M. Perelomov, “Explicit solution of the Calogero model in classical case and geodesic flows on symmetric spaces of zero curvature”, Lettere al Nuovo Cimento, 16:11 (1976), 333–339 | DOI | MR

[49] A. P. Veselov, “Konechnozonnye potentsialy i integriruemye sistemy na sfere s kvadratichnym potentsialom”, Funkts. analiz, 14:1 (1980), 48–50 | MR | Zbl