zbMATH — the first resource for mathematics

Generalized implicit function theorem with applications to some small divisor problems. II. (English) Zbl 0334.58009

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57R30 Foliations in differential topology; geometric theory
58C15 Implicit function theorems; global Newton methods on manifolds
37C75 Stability theory for smooth dynamical systems
37D99 Dynamical systems with hyperbolic behavior
PDF BibTeX Cite
Full Text: DOI
[1] Zehnder, Comm. Pure Appl. Math. 28 pp 91– (1975)
[2] Moser, Nachr. Akad. Wiss., Göttingen, Math. Phys. Kl. pp 1– (1962)
[3] Moser, Math. Ann. 169 pp 136– (1967)
[4] Moser, Proc. Nat. Acad. Sciences 47 pp 11– (1961)
[5] 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] On a class of quasi-periodic solutions for Hamiltonian systems, IMPA, Dynamical Systesm edited by Academic Press, New York and London, 1973, pp. 281–289.
[7] Stable and Random Motions in Dynamical Systems, Princeton University Press, 1973.
[8] 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] 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, Uspehi. Math. Nauk. 18 pp 13– (1963)
[11] Russian Math. Surveys 18 pp 9–
[12] Arnol’d, Uspehi. Math. Nauk 18 pp 91– (1963)
[13] Russian Math. Surveys 18 pp 85–
[14] and , Ergodic problems of Classical Mechanics, Benjamin Inc., New York, 1968, p. 91. · Zbl 0167.22901
[15] Kleine Nenner I: Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl., 1970, pp. 67–105. · Zbl 0201.11202
[16] Kleine Nenner II: Bemerkungen zur Newton’schen Methode Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl., 1972, pp. 1–10.
[17] Rüssmann, Springer, Lecture Notes in Physics 38 pp 598–
[18] Graff, Jour. of Differential Equations. 15 pp 1– (1974)
[19] and , Foundations of Mechanics, W. A. Benjamin, New York, 1967.
[20] Zehnder, Comm. Pure Appl. Math. 26 pp 131– (1973)
[21] Unstability phenomena at Stable equilibrium points, to be published.
[22] Zehnder, Math. Annatlen 219 pp 105– (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.