Abstract
CONSIDER a conservative dynamical system with n degrees of freedom for a fixed value of the energy constant. Suppose that the corresponding (2n – 1)-dimensional energy surface, S, has a finite (2n – 1)-dimensional volume measure. Through every point P of S there is a solution path; its point belonging to the time t will be denoted by Pt. According to the classical definition of Lagrange and Dirichlet, the solution path Pt, – ∞ < t < + ∞, is called stable (with reference to the isoenergetic system), if the distance between the points Pt and Qt remains arbitrarily small along the infinite t-axis whenever the initial position Q is sufficiently close to P.
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References
Birkhoff, G. D., Proc. Nat. Acad. Sci., 17, 656–660 (1931).
Wintner, A., Proc. Nat. Acad. Sci., 18, 248–251 (1932).
Wintner, A., and Hartman, P., Amer. J. Math., 61, 977–984 (1939).
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WINTNER, A. Distributional Stability. Nature 145, 225–226 (1940). https://doi.org/10.1038/145225a0
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DOI: https://doi.org/10.1038/145225a0
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