Интегрируемые гамильтоновы системы - Болсинов А.В.
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[355] Peixoto М. M. Structural stability on two-dimensional manifolds. I, II. // Topology, 1962, v. 1, №2, pp. 101-120; Topology, 1963, v. 2, №2, pp. 179-180.
[356] Peixoto М. C., Peixoto М. M. Structural stability in the plane with enlarged boundary conditions. // Anais Acad. Brasil. Ciencias, 1959, v. 31, №2, pp. 135-160.
[357] Piovan L. Cyclic coverings of Abelian varietes and the Goryachev-Chapygin top. // Math. Ann, 1992, v. 294, pp. 755-764.
[358] Poincare H. Les Methodes Nouvelles de la Mechanique Celeste. Vols. 1-3, Gauthier-Villars, Paris, 1892/1893/1898. Reprint: Dover, New York, 1957.
[359] Poisson L. Memoire sur la variation des constantes arbitrages dans les questions de la mechanique. // Journal de l’Ecole Polytechnique, 1809, 8 (15 cahier).
[360] Polyakova L. S. Topological invariants for some algebraic analogs of the Toda lattice. // In: Advances in Soviet Mathematics. Amer. Math. Soc. v. 6, 1991, pp. 185-208.
[361] Raffy M. L. Determination des elements lineaires doublement harmoniques. // J. de Math., 4 ser., 10(1894).
[362] Reeb G. Sur les points singuliers d’une forme de Pfaff completement integrable ou d’une founction numerique. // Comptec Rendus Acad.Sciences Paris. 1946, v. 22, pp. 847-849.
[363] Reiman A. G., Semenov-Tian-Shansky M. A. A new integrable case of the motion of the 4-dimensional rigid body. // Commun. Math. Phys. 1986, v. 105, pp. 461-472.
[364] Russmann H. Uber das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nahe einer Gleichwichtslosung. // Math. Ann. 1964, v. 154, pp. 284-300.
[365] Schlichenmaier Martin. An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces. // Lecture Notes in Physics, Springer-Verlag, 1989, v. 322.
[366] Scott P. The geometries of 3-manifolds. // Bull. Amer. Math. Soc. 1983, v. 15, pp. 401-487.
[367] Seifert H., Weber C. Die beiden Dodekaederraume. // Math. Zeitschrift, B. 37 (1933), S. 237-253.
Литература
441
[368] Selivanova Е. N. Topological classification of integrable Bott geodesic flows on the two-dimensional torus. // In: Advances in Soviet Mathematics. Amer. Math. Soc. v. 6, 1991, pp. 209-228.
[369] Siegel C.L. On the integrals of canonical systems. // Ann. Math., 1941, 42, pp. 806.
[370] Smale S. Topology and mechanics. I. // Inventiones Mathematicae, 1970, v. 10, pp. 305-331. II. // Inventiones Mathematicae, 1970, v. 11, pp. 45-64.
[371] Smale S. On gradient dynamical systems. // Annals of Math., 1961, v. 74, pp. 199-206.
[372] Spatzier R. J. Riemannian Manifolds with Completely Integrable Geodesic Flows. // Proceedings of Symposia in Pure Mathematics. Amer. Math. Soc. 1993, v. 54, Part 3, pp. 599-608.
[373] Steklov V. A. Remarque sur un probleme de Clebsch sur le movement d’un corps solide dans un liquide indefini et sur le probleme de M. de Brun. // Comptes Rendus de l’Acad.sci., Paris, 1902, 135, pp. 526-528.
[374] Sternberg S. Lectures on Differential Geometry. Prentice Hall, Inc. Englewood Cliffs, N.J. 1964.
[375] Taimanov I. A. Integrable geodesic flows of non-holonomic metrics, (to appear).
[376] Takahashi S. Numerical calculation of the orbital invariant of Goryachev-Chaplygin and Lagrange systems. // In: Fomenko A. Т., Kunii T. L. Topological Modeling for Visualization. Springer-Verlag, 1997, pp. 349-377
[377] Thimm A. Integrable geodesic flows on homogeneous spaces. // Ergod. Theory and Dynam. Syst. 1981, v. 1, №4, pp. 495-517.
[378] Thurston W. P. The Geometry and Topology of 3-Manifolds. Preprint, 1981.
[379] Thurston W. P. Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. // Bull. Amer. Math. Soc., 1982, v. 6, №3, pp. 357-381.
[380] Thurston W. P. Existence of codimension-one foliations. // Ann. Math. 1976, v. 104, № 2, pp. 249-268.
[381] Toda M. Theory of nonlinear lattices. Springer, Berlin, 1981.
[382] Topological Classification of Integrable Systems. // In: Advances in Soviet Mathematics. Editor A. T. Fomenko. Amer. Math. Soc. v. 6, 1991.
[383] Trofimov V. V. Symplectic connections and Maslov-Arnold characteristic classes, j j In: Advances in Soviet Mathematics. Amer. Math. Soc. v. 6, 1991, pp. 257-266.
442
Литература
[384] Vey J. Sur certain systemes dynamiques separables. // Amer. J. Math., 1978, v. 100, pp. 591-614.
[385] Veselov A. P. Two remarks about the connection of Jacobi and Neumann integrable systems. // Math. Zeitschrift, 216 (1994), pp. 337-345.
[386] Waldhausen F. Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I,II. // Invent. Math. 1967, v. 3, №4, pp. 308-333; 1967, v. 4, №2, pp. 88-117.
[387] Wang X. The C*-algebras of Morse-Smale flows on two-manifolds, Ergod. Th. and Dynam. Sys., 1990, v. 10, pp. 565-597.
[388] Weinstein A. Symplectic geometry. // Bulletin of the American Mathematical Society, 1981, v. 5, pp. 1-13.
[389] Weeks J. Hyperbolic structures of three-manifolds. // Ph. Dr. Thesis. Department of Mathematics, Princeton University, 1985.
