Пуассоновые структуры алгебры ли в гамильтоновой механике - Борисов А.
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[291] Minkowski H. Uber die Bewegung eines festen Korpers in einer Flussigkeit. Sitzungsber. Konig. Preuss. Akad. Wiss., v. 30, 1888, p. 1095 1110.
[292] van Moerbeke P. Introduction to algebraic integrable systems and their Painleve analysis. Bowdoin AMS Summer Symp., August 1987, p. 1-48.ЛИТЕРАТУРА
455
[293] Moser J. Lectures on Hamiltonial systems. Mem. Ams., 1968, №81, p. 1-60. (пер. на русс, язык МозерЮ. Лекции о гамильтоновых системах, M.: Мир, 1973, 168 е.).
[294] Moser,!. Three integrable Hamiltonial systems connected, with isospectral deformations. Adv. Math., v. 16, 1975. p. 197-220.
[295] Nambu Y. Generalized Hamiltonian dynamics. Phys. Rev. D, v. 7, 1973, №8, p. 2405-2412.
[296] Nijenhuis A. X n-i-forming sets of eigenvectors. Proc. Kon. Ned. Akad., Amsterdam, v. 54, 1951, p. 200-212.
[297] OhY.-G. Some remarks on the transverse Poisson structures of coadjoint orbits. Lett. Math. Phys., 1986, №12, p. 87-91.
[298] OevelW., Ragnisco O. R-matric.es and higher Poisson brackets for integrable systems. Physica A, v. 161, 1989, p. 181-220.
[299] Olshanetsky M. A., Perelomov A. M. Completely integrable Hamil-tonian systems connected with semi-simple Lie algebras. Invent. Math., v. 37, 1976, №2, p. 93-108.
[300] Olvcr P. Canonical forms and integrability of bi-Hamiltonian systems. Phys. Lett. A, v. 148, 1990, №3,4, p. 177-187.
[301] Orel 0. E., Ryabov P. E. Bifurcation sets in a problem on motion of a rigid body in fluid and in the generalization of this problem. Reg. & Ch. Dynamics, v. 3, 1998, №2, p. 82-93.
[302] Penskoi'A. V. The Volterra lattice as a gradient flow. Reg. & Ch. Dynamics, v. 3, 1998, № 1, p. 76-77.
[303] Perelomov A. M., RagniscoO., Wojciechowski S. Integrability of two interacting n-dimensional rigid bodies. Comm. Math. Phys., v. 102, 1986, p. 573-583.
[304] Plank M. Hamiltonian structures for the n-dimensional Lotka— Volterra equations. J. Math. Phys., v. 36(7), 1995, p. 3520-3534.
[305] Plank M. Bi-Hamiltonian system and Lotka—Volterra equations: a three-dimensional classification. Nonlinearity, v. 9, 1996, p. 887-896.456 ЛИТЕРАТУРА
[306] Poiiicare Н. Theorie des tourbillions. Paris, Carre, 1893.
[307] Poincare H. Sur Ie forme nouvelle des equations de Ia mecanique. C. R. Acad. Sei. Paris, v. 132, 1901, p. 369-371.
[308] Poincare H. Sur la precession des corps deformables. Bull. Astr., v. 27, 1910, p. 321-356.
[309] Reyman A. G., Semenov-Tian-Shansky M. A. Reduction of Hamil-tonian systems, affine Lie algebras and Lax equations I, II. Invent. Math., v. 54: 63, 1979, 1981, p. 81-100: 423-432.
[310] Rcyman A. G., Scmcnov-Tian-Shansky M. A. A new integrable case of the motion of the dimensional rigid, body. Comm. Math. Phys., v. 105, 1986, p. 461-472.
[311] Reyman A. G., Semenov-Tian-Shansky M. A. Compatible Poisson structures for Lax equations: a r-matrix approach. Phys. Lett., v. 130, 1988, p. 456-460.
[312] Reyman A. G., Semenov-Tian-ShanskyM. A. Lax representation with a spectral parameter for the Kowalewski top and its generalizations. Lett. Math. Phys., v. 14, 1987, p. 55 61.
[313] Rott N. Three-vortex motion with zero total circulation. J. of Appl. Math, and Phys. (ZAMP), v. 40, 1989, p. 473-500. Addendum by H.Aref.
[314] Ruijsenaars S. N. M. Relativistic Toda system. Comm. Math. Phys., v. 133, 1990, p. 217-247.
[315] Rumyantsev V. V., Sumbatov A. V. On the problem of generalization of the Hamilton—Jacoby method for nonholonomic systems. ZAMM, v. 58, 1978, p. 477-481.
[316] Sattinger D. H., Weaver O.L. Lie groups and algebras with applications to physics, geometry and mechanics. Springer-Verlag, 1986.
[317] SiniakovN.N. Dynamics of two veHices in circular domain. Reg. & Ch. Dynamics, v. 3, 1998, №4 (to appear).ЛИТЕРАТУРА 457
[318] Sla,wianowski J. Bertrand systems on so('S,R), su(2). Bull, de TAeademie Poloniea des Sciences, v. XXVIII, 1980, №2, p. 83-94.
[319] Souriau J. M. Structure des systemes dynamiques. Dunod, Paris, 1970.
[320] StekloffW. Remarque sur un probleme de Clebsch sur Ie mouvement d'un corps solide dans un liqiude indefini en sur Ie probleme de M. de Brun. Comptes rendus., v. 135, 1902, p. 526-528.
[321] StekloffV. A. Sur Ie mouvement d'un corps solide ayant, une cavite de forme ellipsoidale remple par un liquide incompressible en sur Ies variations des latitudes. Ann. dc la fac. des Seien: de Toulouse, Scr З, v. 1, 1909.
[322] SurisY.B. Integrable discretisations for lattice systems; local equations of motion and, their hamiltonian, properties. Bremen, Germany, preprint, 1997.
[323] Sutherland B. Exact results for a, quantum, many-body problem, in one-dimension. Phys. Rev. A, v. 5, 1972, p. 1372-1376.
[324] Symes W. W. Hamiltonian group actions and integrable systems. Physica D, v. 1, 1980, p. 339-374.
[325] Synge J. L. On the motion of three vortices. Can. J. Math., v. 1, 1949, p. 257-270.
[326] Takhtajan L. A. A simple example of modular forms as tau-functions for integrable equations. Theor. and Math. Phys., v. 93, 1992, №2, p. 330-341.