Generalized implicit function theorems with applications to some small divisor problems, II
1976; Wiley; Volume: 29; Issue: 1 Linguagem: Inglês
10.1002/cpa.3160290104
ISSN1097-0312
Autores Tópico(s)Nonlinear Waves and Solitons
ResumoCommunications on Pure and Applied MathematicsVolume 29, Issue 1 p. 49-111 Article Generalized implicit function theorems with applications to some small divisor problems, II† E. Zehnder, E. Zehnder University of ErlangenSearch for more papers by this author E. Zehnder, E. Zehnder University of ErlangenSearch for more papers by this author First published: January 1976 https://doi.org/10.1002/cpa.3160290104Citations: 107 † Part of this work has been presented in a seminar conducted by L. Nirenberg in the Spring of 1974 at the Courant Institute of Mathematical Sciences. Reproduction in whole or in part is permitted for any purpose of the United States government. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Zehnder, E., Generalized implicit function theorems with applications to some small divisor problems. I., Comm. Pure Appl. Math., Vol. 28, 1975, pp. 91–140. 2 Moser, J., On invariant curves of area preserving mappings of an annulus, Nachr. Akad. Wiss., Göttingen, Math. Phys. Kl. II, 1962, pp. 1–20. 3 Moser, J., Convergent series expansions for quasiperiodic motions, Math. Ann. 169, 1967, pp. 136–176. 4 Moser, J., A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sciences, Vol. 47, 11, 1961, pp. 1824–1831. 5 Moser, J., On the construction of almost periodic solutions for ordinary differential equations, Proc. of the International Conference on Functional Analysis and Related Topics, Tokyo, 1969, pp. 60–67. 6 Moser, J., On a class of quasi-periodic solutions for Hamiltonian systems, IMPA, Dynamical Systesm edited by M. Peixoto, Academic Press, New York and London, 1973, pp. 281–289. 7 Moser, J., Stable and Random Motions in Dynamical Systems, Princeton University Press, 1973. 8 Kolmogorov, A. N., Théorie générale des systèmes dynamiques et mecanique classique, Proc. Int'l. Congress of Math., Amsterdam, 1957, (Translation in Appendix D of R. Abraham, Foundations of Mechanics, Benjamin, 1967). 9 Arnol'd, V. I., Small divisors I; On mappings of a circle onto itself Izvest. Akad. Nauk, Ser. Math. 25, No. 1, 1961, pp. 21–86. Transl Amer. Math Soc. Series 2, Vol. 46, pp. 213–284. 10 Arnol'd, V. I., Proof of a theorem of A. N. Kolmogorov on the invariance of quasiperiodic motions under small perturbations of the Hamiltonian Uspehi. Math. Nauk., 18, 1963, pp. 13–40. Russian Math. Surveys, Vol. 18, No. 5, pp. 9–36. 11 Arnol'd, V. I., Small denominators and problems of stability of motions in classical and celestial mechanics, Uspehi. Math. Nauk, Vol. 18, No. 6, 1963, pp. 91–196. Russian Math. Surveys, Vol. 18, No. 8, pp. 85–193. 12 Arnol'd, V. I., and Avez, A., Ergodic problems of Classical Mechanics, Benjamin Inc., New York, 1968, p. 91. 13 Rüssmann, H., Kleine Nenner I: Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl., 1970, pp. 67–105. 14 Rüssmann, H., Kleine Nenner II: Bemerkungen zur Newton'schen Methode Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl., 1972, pp. 1–10. 15 Rüssmann, H., On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus, Springer, Lecture Notes in Physics, Vol. 38, pp. 598–624. 16 Graff, S. M., On the continuation of hyperbolic invariant tori for Hamiltonian systems Jour. of Differential Equations., 15, 1, 1974, pp. 1–70. 17 Abraham, R., and Marsden, J., Foundations of Mechanics, W. A. Benjamin, New York, 1967. 18 Zehnder, E., Homoclinic points near elliptic fixed points, Comm. Pure Appl. Math., Vol. 26, 1973, pp. 131–182. 19 Zehnder, E., Unstability phenomena at Stable equilibrium points, to be published. 20 Zehnder, E., Moser's implict function theorem in the framework of analytic smoothing, Math. Annatlen 219, 1976, pp. 105–121. Citing Literature Volume29, Issue1January 1976Pages 49-111 ReferencesRelatedInformation
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