Abstract
The connection between nonlinear autonomous dynamic systems, limit cycles, and one-parameter groups of transformations is described. To illustrate the approach, an example is given.
Similar content being viewed by others
References
GlansdorffP. and PrigogineI., Thermodynamic Theory of Structure, Stability and Fluctuations, J. Wiley Intersc., New York, 1971, p. 240.
Van derPolB., Phil. Mag. 2, 978 (1926).
KrogdahlW.S., Astrophys. J. 122, 43 (1955).
BlaquiereA., Nonlinear System Analysis, Academic Press, New York, 1966.
e SilvaJ.A., FerF., LerusteP., and LochakG., C.R. Acad. Sci. Paris 251, 2662 (1960).
PavlidisT., Biological Oscillators: Their Mathematical Analysis, Academic Press, New York, 1973.
NicolisG. and PortnowJ., Chem. Rev. 73, 365 (1973).
TondeurP., Introduction to Lie Groups and Transformation Groups, Springer Verlag, Berlin, 1969.
Steeb, W.-H., Phys. Letters A (1977), in press.
CohenA., An Introduction to the Lie Theory of One-parameter Groups, D.C. Heath, Boston, 1911.
InceE.L., Ordinary Differential Equations, Dover, New York, 1956, p. 112.
BlumanG.W. and ColeJ.D., Similarity Methods for Differential Equations, Springer, New York, 1974, p. 100.
DreitleinJ. and SmoesM.L., J. Theor. Biol. 46, 559 (1974).
AbrahamR., Foundations of Mechanics, W.A. Benjamin, New York, 1967, p. 40, p. 51.
KummerM., J. Math. Phys. 12, 4 (1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Steeb, W.H. Nonlinear autonomous dynamic systems, limit cycles, and one-parameter groups of transformations. Lett Math Phys 2, 171–174 (1977). https://doi.org/10.1007/BF00398584
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00398584