A rapidly convergent iteration method and non-linear differential equations = II

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1. 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. Zbl0011.35202JFM61.0541.02
2. 2 K.O. Friediuchs, Sytmmetric Hyperbolic Linear Differential Equations. Comm. Pure Appl. Math.7, 1954, pp. 345-392. Zbl0059.08902MR62932
3. 3 I. Nash, The Imbedding of Riemannian Manifolds, Ann. Math.63, 1956, pp. 20-63. Zbl0070.38603
4. 4 J. Schwartz, On Nash' s Implicit Function Theorem, Comm. Pure Appl. Math13, 1960, pp. 509-530. Zbl0178.51002MR114144
5. 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. Zbl0104.30503MR132859
6. 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. Zbl0107.29301MR147741
7. 5 G.L. Siegel, Iteration of Analytic Functions. Ann. of Math.43, 1942, pp. 647-612. Zbl0061.14904MR7044
8. 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. Zbl0047.32901MR57407
9. 6 A.N. Kolmogorov, Doklad. Akad., Nauk USSR98, 1954, pp. 527-530. Zbl0056.31502MR68687
10. 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. Zbl0095.17103
11. 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. MR140699
12. 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. MR170705
13. 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. Zbl0129.16606MR163025
14. 11 K.O. Friedrighs, Symmetric Positive Linear Differential Equations, Comm. Pure Appl. Math.11, 1958, pp. 333-418. Zbl0083.31802MR100718
15. 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. Zbl0137.28406
16. 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. 111161. Zbl0109.31401MR142853
17. 13' S.P. Diliberto, Perturbation Theory of Invariant Surfaces I-IV. Mimeographed ONR Reports, Berkeley, 1956/57. 
18. 14 Kyner, W.T., Invariant manifolds, Rend. del Circolo MatematicoPalermo, Ser. II, Vol. 9, 1961, pp. 98-110. Zbl0104.06303MR149038
19. 14' J.K. Hale, Integral Manifolds of Perturbed Differential Systems, Annals of Math., 78. 1961, pp. 496-531. Zbl0163.32804MR123786
20. 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. Zbl0117.05403MR162036
21. 16 L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, 13 (1959), pp. 116-162. Zbl0088.07601MR109940
22. 17 Gagliardo, E., Ulteriori proprieta di alcune classi di funzioni in più variabili, Ricerche Mat, 8, 1959, pp. 24-51. Zbl0199.44701MR109295
23. 18 J.J. Kohn and L. Nirenberg, Non-coercive boundary value problems to appear in Comm. Pure Appl. Math. (See under « elliptic regularization »). Zbl0125.33302MR181815
24. 19 W.T. Kyner, A fixed point theorem. Contributions to the Theory on Vonlinear Oscillations, Vol. 3, Princeton University Press, Annals of Math. Studies36, 1956, pp. 197-205. Zbl0073.33501MR81472
25. 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. Zbl0082.30103MR101946
26. 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. 
27. 22 C.L. Siegel, Verlesungen über Himmelsmechanik, Springer, 1956. MR80009
28. 23 H. Cremer, Über die Hänfigkeit der Niehtzentren, Math. Ann.115, pp. 607-612, 1942. Zbl0018.36802JFM64.0289.02
29. 24, N. Levinson, Transformation of an analytic function of several zariables to a canonical form.Duke Math. Journal28, 1961, pp. 345-353. (See Theorem 2). Zbl0100.29002MR145101
30. 25 N.I. Achieser, Vorlisungen iiber Approximationstheorie, Akd, Verlag. Berlin1953, translated from Russian, Chapter V. Zbl0052.29002MR61692

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