A rapidly convergent iteration method and non-linear differential equations = II
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 20 (1966) no. 3, p. 499-535
@article{ASNSP_1966_3_20_3_499_0,
     author = {Moser, J\"urgen},
     title = {A rapidly convergent iteration method and non-linear differential equations = II},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 20},
     number = {3},
     year = {1966},
     pages = {499-535},
     mrnumber = {206461},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1966_3_20_3_499_0}
}
Moser, Jürgen. A rapidly convergent iteration method and non-linear differential equations = II. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 20 (1966) no. 3, pp. 499-535. https://www.numdam.org/item/ASNSP_1966_3_20_3_499_0/

1 J. Schauder, Das Anfangsvertproblem einer quasi-linearen hyperbolischen Differentialgleichung zweiter Order in beliebige), Anzahl von unabhängigen Veränderlichen. Fund. Math. 24, 1935, pp. 213-246. | JFM 61.0541.02 | Zbl 0011.35202

2 K.O. Friediuchs, Sytmmetric Hyperbolic Linear Differential Equations. Comm. Pure Appl. Math. 7, 1954, pp. 345-392. | MR 62932 | Zbl 0059.08902

3 I. Nash, The Imbedding of Riemannian Manifolds, Ann. Math. 63, 1956, pp. 20-63. | Zbl 0070.38603

4 J. Schwartz, On Nash' s Implicit Function Theorem, Comm. Pure Appl. Math 13, 1960, pp. 509-530. | MR 114144 | Zbl 0178.51002

4' J. Moser, A. New Technique for the Construction of Solutions of Nonlinear Differential Equations. Proc. Nat. Acad. Sciences, Vol. 47, No. 11, pp. 1824-1831, 1961. | MR 132859 | Zbl 0104.30503

4" J. Moser, On Invariant Curves of Area-Preserving Mappings of an Annulus. Nachr. Akad. Wiss. Göttingen Math. Phys. K1. IIa, No. 1, 1962, pp. 1-20. | MR 147741 | Zbl 0107.29301

5 G.L. Siegel, Iteration of Analytic Functions. Ann. of Math. 43, 1942, pp. 647-612. | MR 7044 | Zbl 0061.14904

5' C.L. Siegel, Über die Normalform Analytischer Differentialgleichungen in der Nähe einer Gleich-gewichtslösung, Nachr. Akad. Wiss., Göttingen, Math. Phys.K1, IIa, 1952, pp. 21-30. | MR 57407 | Zbl 0047.32901

6 A.N. Kolmogorov, Doklad. Akad., Nauk USSR 98, 1954, pp. 527-530. | MR 68687 | Zbl 0056.31502

7 A.N. Kolmogorov, General Theory of Dynamical Systeans and Classical Mechanics. Proc. of Intl. Congress of Math., Amsterdam, 1954, (Amsterdam: Erven P. Nordhoff, 1957), Vol. 1, pp. 315-333. | Zbl 0095.17103

8 V.I. Arnold, @@ Small divisors » I, On mappings of a circle onto itself, Isvest. Akad. Nauk, ser. mat., 25, No. 1, 1961, pp. 21-76. | MR 140699

9 V.I. Arnold, Small Divisor and Stability Problemis in Classicat and Celestial Mechanics. Uspekhi Mat. Nauk USSR, Vol. 18, Ser. 6 (119), 1963, pp. 81-192. | MR 170705

10 V.I. Arnold, Proof of A. N. Kolmogorov's Theorem on the Preservation of Quasi-Periodic Motions under Small Perturbation of the Hamiltonian, Uspekhi Mat. N. USSR, Vol. 18, Ser. 5 (113), 1963, pp. 13-40. | MR 163025 | Zbl 0129.16606

11 K.O. Friedrighs, Symmetric Positive Linear Differential Equations, Comm. Pure Appl. Math. 11, 1958, pp. 333-418. | MR 100718 | Zbl 0083.31802

12 N.N. Bogolioubov, and Y.A. Mitropolski, The Method of Intergral Manifolds in Nonlinear Mechanics, Contrib. to Differential Equations, Vol. II, 1963, pp. 123-196. | Zbl 0137.28406

13 S.P. Diliberto, Perturbation Theorems for Periodic Surfaces I, Rend. del Cire. Mat. Palermo (2), 9, 1961, pp. 265-299. II, Rend. del Circ. Mat. Palermo (2), 10, 1962, pp. 111 161. | MR 142853 | Zbl 0109.31401

13' S.P. Diliberto, Perturbation Theory of Invariant Surfaces I-IV. Mimeographed ONR Reports, Berkeley, 1956/57.

14 Kyner, W.T., Invariant manifolds, Rend. del Circolo Matematico Palermo, Ser. II, Vol. 9, 1961, pp. 98-110. | MR 149038 | Zbl 0104.06303

14' J.K. Hale, Integral Manifolds of Perturbed Differential Systems, Annals of Math., 78. 1961, pp. 496-531. | MR 123786 | Zbl 0163.32804

15 I. Kupka, Stabilité des varietés invariantes d'un champ de vecteurs pour les petites perturbations. Compt. Rend. Acad. Sc. Paris, 258, Group 1, 1964, pp. 4197-4200. | MR 162036 | Zbl 0117.05403

16 L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), pp. 116-162. | Numdam | MR 109940 | Zbl 0088.07601

17 Gagliardo, E., Ulteriori proprieta di alcune classi di funzioni in più variabili, Ricerche Mat, 8, 1959, pp. 24-51. | MR 109295 | Zbl 0199.44701

18 J.J. Kohn and L. Nirenberg, Non-coercive boundary value problems to appear in Comm. Pure Appl. Math. (See under « elliptic regularization »). | MR 181815 | Zbl 0125.33302

19 W.T. Kyner, A fixed point theorem. Contributions to the Theory on Vonlinear Oscillations, Vol. 3, Princeton University Press, Annals of Math. Studies 36, 1956, pp. 197-205. | MR 81472 | Zbl 0073.33501

20 W.T. Kyner, Small Periodic Perturbations of an Autonomous System of Vector- Equations. Contributions to the Theory of Nonlinear Oscillations, Vol. 4, Princeton, 1958. | MR 101946

21 R. Sacker, On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations, NYU Report, IMM-NYU 333, Oct. 1964, to be published in Comm. Pure Appl. Math.

22 C.L. Siegel, Verlesungen über Himmelsmechanik, Springer, 1956. | MR 80009

23 H. Cremer, Über die Hänfigkeit der Niehtzentren, Math. Ann. 115, pp. 607-612, 1942. | JFM 64.0289.02 | Zbl 0018.36802

24, N. Levinson, Transformation of an analytic function of several zariables to a canonical form. Duke Math. Journal 28, 1961, pp. 345-353. (See Theorem 2). | MR 145101 | Zbl 0100.29002

25 N.I. Achieser, Vorlisungen iiber Approximationstheorie, Akd, Verlag. Berlin 1953, translated from Russian, Chapter V. | MR 61692 | Zbl 0052.29002