Moser, Jürgen Periodic orbits near an equilibrium and a theorem by Alan Weinstein. (English) Zbl 0346.34024 Commun. Pure Appl. Math. 29, 727-747 (1976); addendum ibid. 31, 529-530 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 113 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics PDF BibTeX XML Cite \textit{J. Moser}, Commun. Pure Appl. Math. 29, 727--747 (1976; Zbl 0346.34024) Full Text: DOI References: [1] Berger, J. Diff. Eq. 10 pp 17– (1971) [2] Braun, J. Diff. Eq. 13 pp 300– (1973) [3] Fenichel, Ind. Univ. Math. J. 21 pp 193– (1971) [4] Fuller, Am. J. Math. 89 pp 133– (1967) [5] The existence of periodic orbits Mimeographed Seminar Notes of the Institut de Recherche Mathematique Avancee, Strassbourg, 1968. [6] Gordon, Journ. Diff. Eq. 10 pp 324– (1971) [7] Oscillations in Nonlinear Systems McGraw Hill 1963. [8] Hopf, Math. Ann. 96 pp 225– (1926) [9] On the Lyapounov sub-center manifold, Appendix C in R. Abraham, Foundations in Mechanics, Benjamin, 1967. [10] Krasnoselskii, Dokl. Akad. Nauk, USSR 103 pp 961– (1955) [11] Liapounoff, Ann. Fac. Sci. 2 pp 203– (1907) · JFM 38.0738.07 [12] Moser, Comm. Pure Appl. Math. 23 pp 609– (1970) [13] A theorem by A. Weinstein and bifurcation theory, Report of the University Louvain la Neuve, Jan. 1976. · Zbl 0351.58002 [14] Periodic orbits near an equilibrium point: the Lyapunov center theorem, Proc. on Long-Time Prediction in Dynamics, held in Aug. 1975, to appear. [15] Nonlinear Functional Analysis, Gordon and Breach, 1969. [16] Seifert, Proc. Am. Math. Soc. 1 pp 287– (1950) [17] and , Lectures on Celestial Mechanics New York, Springer, 1971. [18] Siegel, Machr. Akad. Wiss. Göttingen, Math-Phys. KI. pp 261– (1971) [19] Sweet, J. Diff. Eq./ 14 pp 171– (1973) [20] Weinstein, Ann. Math. 98 pp 377– (1973) [21] Weinstein, Inv. Math. 20 pp 47– (1973) 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.