References
J. A. Yorke,Asymptotic properties of solutions using the second derivative of a liapunov function, Dissertation, Univ. of Maryland, 1967.
M. B. Kudaev, A study of the behavior of the trajectories of systems of differential equations by means of Lyapunov functions (Russian),Dokl. Akad. Nauk. SSSR 147 (1962), 1285–1287.
M. B. Kudaev, Classification of multi-dimensional systems of ordinary differential equations by the method of Lyapunov functions (Russian),Diff. Uravnen. 1 (1965), 346–356 [Differential Equations 1 (1965), 263–269].
Edwin H. Spanier,Algebraic Topology, McGraw-Hill, New York, 1966.
Sze-Tsen Hu,Homotopy Theory, Academic Press, New York, 1949.
N. P. Bhatia andG. P. Szegö,Dynamical Systems: Stability Theory and Applications, Springer-Verlag, Berlin, New York, 1967.
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This research was partially supported by National Science Foundation Grant GP-9347.
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Yorke, J.A. A theorem on Liapunov functions using\(\ddot V\) . Math. Systems Theory 4, 40–45 (1970). https://doi.org/10.1007/BF01705884
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DOI: https://doi.org/10.1007/BF01705884