Abstract
I wish to take this opportunity to initiate a systematic study of what we shall, following HAJEK [18], call Semi-Dynamical Systems.
Partial support of the author by the National Science Foundation Grant No. NSF-GP-7447 is gratefully acknowledged.
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References
H. Poincare, “Les méthodes nouvelles de la mecaniques celeste” Gauthier-Villars, Paris (1892–1899). Reprint, Dover, New York.
Ivar Bendixon, Sur les courbes definies par des equations differentielles, Acta Mathematica, 24 (1901), 1-88.
A.M. Lyapunov, “Probleme génerai de la stabilite du mouvement”, Annals of Mathematics Studies, No. 17, Princeton, 1947.
G.D. Birkhoff, “Dynamical Systems”, American Mathematical Society Colloquium Publications, Vol. 9 New York, 1927.
V.V. Nemytskii and V.V. Stepanov, “Qualitative Theory of Differential Equations”, Princeton University Press, Princeton, 1960. Original Russian 1947, 1949.
V.V. Nemytskii, Topological Problems of the Theory of Dynamical Systems, Uspehi Mat. Nauk., 4 (1949), 91–153 (Russian); English Translation: Am. Math. Soc. Translations, No. 103, (1954).
N.P. Bhatia and G.P. Szegö, “Dynamical Systems: Stability Theory and Applications”, Lecture Notes in Mathematics, No. 35, Springer-Verlag, Berlin-Heidelberg-New York, 1967.
V.I. Zubov, “Methods of A.M. LYAPUNOV and Their Application”, Noordhoff, Groningen, The Netherlands, 1964; Original Russian, 1957.
T. Ura, Surle courant exterieur a unse region invariante; Prolongements d’une caracteristique et l’ordre de stabilite, Funkcialaj Ekvacioj, Vol, 2 (1959), 143–200.
T. Ura, On the flow outside a closed invariant set, stability, relative stability and saddle sets, Contributions to Differential Equations, 3 (1964), 249–294.
J. Auslander and P. Seibert, Prolongations and Stability in Dynamical Systems, Annales de l’Institut Fourier, 14 (1964), 237–267.
N.P. Bhatia, On Asymptotic Stability in Dynamical Systems, Mathematical Systems Theory, 1 (1967), 113–127.
N.P. Bhatia, Weak Attractors in Dynamical Systems, Bol. Soc. Mat. Mex., 11,(1966), 56–64.
N.P. Bhatia and G.P. Szegö, Weak Attractors in Rn, Mathematical Systems Theory, 1 (1967), 129–133.
N.N. Krasovskii, “Stability of Motion”, Stanford Univ. Press, Stanford, 1963; Original Russian, 1959.
J.K. Hale, A Class of Functional-Differential Equations, Contributions to Differential Equations, 1, (1963), 411–423.
J.K. Hale, Sufficient Conditions for Stability and Instability of Autonomous Functional-Differential Equations, J. of Differential Equations, 1 (1965), 452–482.
O. Hajek, Structure of Dynamical Systems, Comm. Math. Univ. Carolinae, 6 (1965), 53–72. Correction same journal, 6 (1965), 211-212.
O. Hajek, Critical Points of Abstract Dynamical Systems, Comm. Math., Univ. Carolinae, 5 (1964), 121–124.
F. Brock Fuller, On the surface of section and periodic trajectories, Amer. J. Math., 87 (1965), 473–480.
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Bhatia, N.P. (1969). Semi-Dynamical Systems. In: Kuhn, H.W., Szegö, G.P. (eds) Mathematical Systems Theory and Economics I / II. Lecture Notes in Operations Research and Mathematical Economics, vol 11/12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46196-5_14
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