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Some remarks on set-valued dynamical systems

Published online by Cambridge University Press:  17 February 2009

J. W. Nieuwenhuis
J. W. Nieuwenhuis
Affiliation:
Econometric Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
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Abstract

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It is shown that under some conditions a collection of continuous mappings gives rise to a set-valued dynamical system. Using this it is further shown that under some other conditions the system ẋ(t) ∈ F(x(t)) is equivalent to a set-valued dynamical system.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 3 , January 1981 , pp. 308 - 313
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Castaing, C. and Valadier, M., “Equations différentielles multivoques dans les espaces localement convexes”, Revue Française d'Informatique et de Recherche Operationelle 16 (1969), 3–16.Google Scholar
[2]Champsaur, P., Dréze, J. and Henry, C., “Stability theorems with economic applications”, Econometrica 45 (1977), 273–294.CrossRefGoogle Scholar
[3]Cherene, L. J. Jr, “Set valued dynamical systems and economic flow”, Lecture Notes in Economics and Mathematical Systems 158 (Springer-Verlag, 1978).Google Scholar
[4]Fleming, W. H. and Rishel, R. W., Deterministic and stochastic optimal control (Springer-Verlag, 1975).CrossRefGoogle Scholar
[5]Hildenbrand, W., Core and equilibria of a large economy (Princeton University Press, Princeton, New Jersey, 1974).Google Scholar
[6]Kloeden, P., “General control systems without backward extension, differential games and control theory”, Lecture Notes in Pure and Applied Mathematics 10 (Marcel Dekker, New York, 1974), 49–58.Google Scholar
[7]Kloeden, P., “General control systems, mathematical control theory”, Lecture Notes in Mathematics 680 (Springer-Verlag, 1978), 119–137.Google Scholar
[8]Kloeden, P., “The funnel boundary of multivalued dynamical systems”, J. Atsstral. Math. Soc. A 27 (1979), 108–124.CrossRefGoogle Scholar
[9]Roxin, E., “Stability in general control systems”, J. Diff. Equations 1 (1965), 115–150.CrossRefGoogle Scholar
[10]Roxin, E., “On generalized dynamical systems defined by contingent equations”, J. Diff. Equations 1 (1965), 188–205.CrossRefGoogle Scholar