Birtea, Petre; Puta, Mircea; Tudoran, Răzvan Micu Periodic orbits in the case of a zero eigenvalue. (English) Zbl 1131.34034 C. R., Math., Acad. Sci. Paris 344, No. 12, 779-784 (2007). The paper deals with a special case for investigating periodic orbits of a dynamic system in the case of zero eigenvalue of the linearized system. It could be considered as a supplement of some results of Moser (1976) and Weinstein (1973) related to this problem. Certain conditions for the existence of periodic solutions are formulated and proved. Two examples are given. Reviewer: Bojidar Cheshankov (Sofia) Cited in 13 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics Keywords:periodic solutions PDFBibTeX XMLCite \textit{P. Birtea} et al., C. R., Math., Acad. Sci. Paris 344, No. 12, 779--784 (2007; Zbl 1131.34034) Full Text: DOI arXiv References: [1] Dubrovin, B.; Krichever, I.; Novikov, S., (Integrable Systems. Integrable Systems, Encyclopedia of Math. Sci., vol. 4 (1990), Springer-Verlag: Springer-Verlag Berlin), 173-280 [2] Lyapunov, M. A., Problème général de la stabilité du mouvement, Ann. Fac. Sci. Toulouse, 2, 203-474 (1907) · JFM 38.0738.07 [3] Moser, J., Periodic orbits and a theorem by Alan Weinstein, Comm. Pure Appl. Math., 29, 727-747 (1976) · Zbl 0346.34024 [4] Weinstein, A., Normal modes for non-linear Hamiltonian systems, Invent. Math., 20, 47-57 (1973) · Zbl 0264.70020 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.