不急，一点一点来

先贴个Arnold推荐的，这个列表是Arnold在Dynamical Systems III Mathematical Aspects of Classical and Celestial Mechanics[Encyclopaedia of Mathematical Sciences3]V.I.Arnold(1988,Springer Berlin Heidelberg)里推荐的

Recommended Reading
[1] Abraham, R.; Marsden, J.E.: Foundations of mechanics. 2nd ed. Reading, Mass.: The
Benjamin/Cummings Publishing Company, Inc. m-XVI, XXII, 806 p. (1978). Zbl. 397.70001
[2] Alekseev, V.M.: Quasirandom dynamical systems. I, 11, III Mat. Sb., Nov. Sero 76, No. 1,
72-134 (1968) (Russian); 77, No. 4, 545-601 (1968) (Russian); 78, No. 1, 3-50 (1968) (Russian);
English transI.: Math. USSR, Sb. 5, No. 1, 73-128 (1968); 6, No. 4, 505-560 (1968);
7, No. 1, 1-43 (1969). Zbl. 198,569; Zbl. 198,570; Zbl. 198,570
[3] Alekseev, V.M.: Final motions in the three-body problem and symbolic dynamics Usp.
Mat. Nauk 36, No. 4, 161-176 (1981) (Russian); English transI.: Russ. Math. Surv. 36,
No. 4, 181-200 (1981). Zbl. 503.70006
[4] Anosov, D. V.: Geodesic flows on c10sed Riemannian manifolds of negative curvature
Tr. Mat. Inst. Steklova 90, 210 p. (1967) (Russian); English transI.: Proc. Steklov Inst.
Math. 90 (1967). Zbl. 163,436
[5] Appell, P.: Traite de mecanique rationnelle. Tomes 1-2. 4e M. Paris: Gauthier-Villars
(1919/1924)
[6] Arnol'd, V. 1.: Proof of A. N. Kolmogorov's theorem on the preservation of quasi-periodic
motions under small perturbations of the Hamiltonian. Usp. Mat. Nauk 18, No. 5, 13-40
(1963) (Russian); English transI.: Russ. Math. Surv. 18, No. 5, 9-36 (1963). Zbl. 129, 166
[7] Arnol'd, V.I.: Small denominators and problems of stability of motion in c1assical and
celestial mechanics. Usp. Mat. Nauk 18, No. 6,91-192 (1963) (Russian); English transI.:
Russ. Math. Surv. 18, No. 6, 85-192 (1963). Zbl. 135,427
[8] Arnol'd, V. I.: Mathematical methods of classical mechanics. Moskva: Nauka. 431 p. (1974).
(Russian); English trans!.: New York-Heidelberg-Berlin: Springer-Verlag. X, 462 p. (1978).
Zbl. 386.70001
[9] Arnol'd, V.I.: Geometrical methods in the theory of ordinary differential equations. Moskva:
Nauka. (1978) (Russian); English trans!.: New York-Heidelberg-Berlin: SpringerVerlag.
XI, 334 p. (1983). Zbl. 507.34003
[10] Birkhoff, G.D.: Dynamical systems. Am. Math. Soc. Colloq. Publ. IX. New York: American
Mathematical Society. VIII, 295 p. (1927).
[11] Bogolyubov, N.N.: On some statistical methods in mathematical physics. L'vov: Akad.
Nauk Ukr. SSR. 139 p. (1945). (Russian)
[12] Bogolyubov, N.N.; Mitropol'skij, Yu.A.: Asymptotic methods in the theory ofnonlinear
oscillations. 2nd ed. Moskva: Nauka. 408 p. (1958). (Russian); English transI.: Delhi: Hindustan
Publ. Corp.; New York: Gordon and Breach Science Publ. V, 537 p. (1961). Zbl.
83,81
[13] Cartan, E.: Leyons sur les invariants integraux. Paris: Hermann. X, 210 p. (1922). Jrb.
48,538
[14] Chaplygin, S.A.: Investigations in the dynamics of nonholonomic systems. Moskva-Leningrad.
(1949). (Russian)
[15] Charlier, c.L.: Die Mechanik des Himmels. Bd. I, 11. 2. Aufl. Berlin: Walter de Gruyter.
VIII, 488 p.; VIII, 478 p. (1927). Jrb. 53, 892
[16] Dirac, P.A.M.: On generalized Hamiltonian dynamics. Can. J. Math. 2, No. 2, 129-148
(1950). Zbl. 36, 141
[17] Hertz, H.: Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt. Ges. Werke,
Bd.3. Leipzig: Barth. (1910). English transI.: New York: Dover Publications, Inc. 274 p.
(1956). Zbl. 74, 388
Recommended Reading 277
[18] Jacobi, c.G.J.: Vorlesungen über Dynamik. Berlin: G. Reimer Verlag (1884)
[19] Karapetyan, A.V.; Rumyantsev, V.V.: Stability of conservative and dissipative systems.
Itogi Nauki Tekh., Sero Obshch. Mekh. 6,132 p. (1983). (Russian). Zbl. 596.70024
[20] Kozlov, V.V.: Methods of qualitative analysis in the dynamics of a rigid body. Moskva:
Izdatel'stvo Moskovskogo Universiteta. 232 p. (1980). (Russian). Zbl. 557.70009
[21] Kozlov, V.V.: Integrability and non-integrability in Hamiltonian mechanics. Usp. Mal.
Nauk 38, No. 1, 3-67 (1983) (Russian); English transI.: Russ. Math. Surv. 38, No. 1, 1-76
(1983). Zbl. 525.70023
[22] Kolmogorov, AN.: On conservation of conditionally periodic motions under small perturbations
of the Hamiltonian. Dokl. Akad. Nauk SSSR 98, No. 4, 527-530 (1954). (Russian).
Zbl. 56, 315
[23] Kolmogorov, AN.: General theory of dynamical systems and classical mechanics. Proc.
Int. Congr. Math, 1954, Amsterdam 1,315-333 (1957). (Russian); English trans!.: Appendix
in [1]. Zbl. 95, 171
[24] Lagrange, 1.L.: Mecanique analytique. (Euvres de Lagrange, Vols. 11-12 Paris: GauthierVillars
(1888-1889)
[25] Moiseev, N.N.: Asymptotic methods of nonlinear mechanics. 2nd ed. Moskva: Nauka.
400 p. (1981). (Russian). Zbl. 527.70024
[26] Moser, 1.: Convergent series expansions for quasi-periodic motions. Math. Ann. 169, 136-
176 (1967). Zbl. 149,299
[27] Moser, 1.: Lectures on Hamiltonian systems. Mem. Am. Math. Soc. 81, 60 p. (1968). Zbl.
172,114
[28] Moser, 1.: Stable and random motions in dynamical systems. Ann. Math. Stud. 77, VIII,
199 p. (1973). Zbl. 271.70009
[29] Moser, 1.: Various aspects of integrable Hamiltonian systems. Dynamical systems,
C. 1. M. E. Lect., Bressanone 1978. Prog. Math. 8, 233-290 (1980). Zbl. 468.58011
[30] Nejmark, Yu.1.; Fufaev, N.A: Dynamics of nonholonomic systems. Moskva: Nauka.
520 p. (1967). (Russian); English transI.: Transl. Math. Monogr., Am. Math. Soc. 33. IX,
518 p. (1972). Zbl. 171,455
[31] Nekhoroshev, N. N.: An exponential estimate of the time of stability of nearly-integrable
Hamiltonian systems. Usp. Mat. Nauk 32, No. 6, 5-66 (1977) (Russian); English trans!.:
Russ. Math. Surv. 32, No. 6,1-65 (1977). Zbl. 383.70023
[32] Nitecki, Z.: Differentiable dynamies. An introduction to the orbit structure of diffeomorphisms.
Cambridge, Mass.-London: The M.1.T. Press. XV, 282 p. (1971). Zbl. 246.58012
[33] Poincare, H.: Les methodes nouvelles de la mecanique celeste. Vols. 1-3. Paris: GauthierVillars.
(1892/1893/1899); New York: Dover Publications, Inc. Vol. I: 382 p.; Vol. 11:
479 p.; Vol. 111: 414 p. (1957). Zbl. 79, 238
[34] Siegel, C. L.: On the integrals of canonical systems, Ann. Math., 11. Sero 42, No. 3, 806-822
(1941). Zbl. 25, 265
[35] Siegel, c.L.: Uber die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen
in der Nahe einer Gleichgewichtslosung. Math. Ann. 128, 144-170 (1954).
Zbl. 57, 320
[36] Siegel, c.L.; Moser, J.: Lectures on celestial mechanics. Berlin-Heidelberg-New York:
Springer-Verlag. XII, 290 p. (1971). Zbl. 312.70017
[37] Smale, S.: Topology and mechanics. I, 11. Invent. Math. 10, No. 6, 305-331 and 11, No. 1,
45-64 (1970). Zbl. 202, 232; Zbl. 203, 261
[38] Variational principles ofmechanics. Collection ofpapers. Moskva: Fizmatgiz. 932 p. (1959).
(Russian). Zbl. 87, 170
[39] Whittaker, E. T.: A treatise on the analytical dynamics of particles and rigid bodies. 4th
ed. Cambridge: Cambridge University Press XIV, 456 p. (1960). Zbl. 91, 164
[40] Williamson, 1.: On the algebraic problem concerning the normal forms oflinear dynamical
systems. Am. 1. Math. 58, No. I, 141-163 (1936). Zbl. 13,284
[41] Williamson, J.: The exponential representation of canonical matrices, Am. J. Math. 61,
No. 4,897-911 (1939). Zbl. 22,100
[42] Wintner, A: The analytical foundations of celestial mechanics. Princeton: Princeton University
Press. XII, 448 p. (1941). Zbl. 26, 23
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